---
_id: '10594'
abstract:
- lang: eng
text: "Multiobjective optimization plays an increasingly important role in modern
applications, where several criteria are often of equal importance. The task in
multiobjective optimization and multiobjective optimal control is therefore to
compute\r\nthe set of optimal compromises (the Pareto set) between the conflicting
objectives.\r\n\r\nSince – in contrast to the solution of a single objective optimization
problem – the\r\nPareto set generally consists of an infinite number of solutions,
the computational\r\neffort can quickly become challenging. This is even more
the case when many problems have to be solved, when the number of objectives is
high, or when the objectives\r\nare costly to evaluate. Consequently, this thesis
is devoted to the identification and\r\nexploitation of structure both in the
Pareto set and the dynamics of the underlying\r\nmodel as well as to the development
of efficient algorithms for solving problems with\r\nadditional parameters, with
a high number of objectives or with PDE-constraints.\r\nThese three challenges
are addressed in three respective parts.\r\n\r\nIn the first part, predictor-corrector
methods are extended to entire Pareto sets.\r\nWhen certain smoothness assumptions
are satisfied, then the set of parameter dependent Pareto sets possesses additional
structure, i.e. it is a manifold. The tangent\r\nspace can be approximated numerically
which yields a direction for the predictor\r\nstep. In the corrector step, the
predicted set converges to the Pareto set at a new\r\nparameter value. The resulting
algorithm is applied to an example from autonomous\r\ndriving.\r\n\r\nIn the second
part, the hierarchical structure of Pareto sets is investigated. When\r\nconsidering
a subset of the objectives, the resulting solution is a subset of the Pareto\r\nset
of the original problem. Under additional smoothness assumptions, the respective
subsets are located on the boundary of the Pareto set of the full problem. This\r\nway,
the “skeleton” of a Pareto set can be computed and due to the exponential\r\nincrease
in computing time with the number of objectives, the computations of\r\nthese
subsets are significantly faster which is demonstrated using an example from\r\nindustrial
laundries.\r\n\r\nIn the third part, PDE-constrained multiobjective optimal control
problems are\r\naddressed by reduced order modeling methods. Reduced order models
exploit the\r\nstructure in the system dynamics, for example by describing the
dynamics of only the\r\nmost energetic modes. The model reduction introduces an
error in both the function values and their gradients, which has to be taken into
account in the development of\r\nalgorithms. Both scalarization and set-oriented
approaches are coupled with reduced\r\norder modeling. Convergence results are
presented and the numerical benefit is\r\ninvestigated. The algorithms are applied
to semi-linear heat flow problems as well\r\nas to the Navier-Stokes equations.\r\n"
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: Peitz S. Exploiting Structure in Multiobjective Optimization and Optimal
Control.; 2017. doi:10.17619/UNIPB/1-176
apa: Peitz, S. (2017). Exploiting structure in multiobjective optimization
and optimal control. https://doi.org/10.17619/UNIPB/1-176
bibtex: '@book{Peitz_2017, title={ Exploiting structure in multiobjective optimization
and optimal control}, DOI={10.17619/UNIPB/1-176},
author={Peitz, Sebastian}, year={2017} }'
chicago: Peitz, Sebastian. Exploiting Structure in Multiobjective Optimization
and Optimal Control, 2017. https://doi.org/10.17619/UNIPB/1-176.
ieee: S. Peitz, Exploiting structure in multiobjective optimization and optimal
control. 2017.
mla: Peitz, Sebastian. Exploiting Structure in Multiobjective Optimization
and Optimal Control. 2017, doi:10.17619/UNIPB/1-176.
short: S. Peitz, Exploiting Structure in Multiobjective Optimization and Optimal
Control, 2017.
date_created: 2019-07-10T08:12:22Z
date_updated: 2022-01-06T06:50:46Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.17619/UNIPB/1-176
file:
- access_level: closed
content_type: application/pdf
creator: speitz
date_created: 2020-03-13T12:52:50Z
date_updated: 2020-03-13T12:52:50Z
file_id: '16298'
file_name: Dissertation_Peitz.pdf
file_size: 16636801
relation: main_file
success: 1
file_date_updated: 2020-03-13T12:52:50Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://d-nb.info/1139356542/34
oa: '1'
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication_status: published
status: public
title: " \tExploiting structure in multiobjective optimization and optimal control"
type: dissertation
user_id: '47427'
year: '2017'
...
---
_id: '16499'
author:
- first_name: Luca
full_name: Biasco, Luca
last_name: Biasco
- first_name: Laura
full_name: Di Gregorio, Laura
last_name: Di Gregorio
citation:
ama: Biasco L, Di Gregorio L. A Birkhoff–Lewis Type Theorem for the Nonlinear Wave
Equation. Archive for Rational Mechanics and Analysis. 2009:303-362. doi:10.1007/s00205-009-0240-y
apa: Biasco, L., & Di Gregorio, L. (2009). A Birkhoff–Lewis Type Theorem for
the Nonlinear Wave Equation. Archive for Rational Mechanics and Analysis,
303–362. https://doi.org/10.1007/s00205-009-0240-y
bibtex: '@article{Biasco_Di Gregorio_2009, title={A Birkhoff–Lewis Type Theorem
for the Nonlinear Wave Equation}, DOI={10.1007/s00205-009-0240-y},
journal={Archive for Rational Mechanics and Analysis}, author={Biasco, Luca and
Di Gregorio, Laura}, year={2009}, pages={303–362} }'
chicago: Biasco, Luca, and Laura Di Gregorio. “A Birkhoff–Lewis Type Theorem for
the Nonlinear Wave Equation.” Archive for Rational Mechanics and Analysis,
2009, 303–62. https://doi.org/10.1007/s00205-009-0240-y.
ieee: L. Biasco and L. Di Gregorio, “A Birkhoff–Lewis Type Theorem for the Nonlinear
Wave Equation,” Archive for Rational Mechanics and Analysis, pp. 303–362,
2009.
mla: Biasco, Luca, and Laura Di Gregorio. “A Birkhoff–Lewis Type Theorem for the
Nonlinear Wave Equation.” Archive for Rational Mechanics and Analysis,
2009, pp. 303–62, doi:10.1007/s00205-009-0240-y.
short: L. Biasco, L. Di Gregorio, Archive for Rational Mechanics and Analysis (2009)
303–362.
date_created: 2020-04-14T09:59:20Z
date_updated: 2022-01-06T06:52:51Z
department:
- _id: '101'
doi: 10.1007/s00205-009-0240-y
language:
- iso: eng
page: 303-362
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
issn:
- 0003-9527
- 1432-0673
publication_status: published
status: public
title: A Birkhoff–Lewis Type Theorem for the Nonlinear Wave Equation
type: journal_article
user_id: '47427'
year: '2009'
...
---
_id: '8758'
abstract:
- lang: eng
text: In this contribution we compare two different approaches to the implementation
of a Model Predictive Controller in an electric vehicle with respect to the quality
of the solution and real-time applicability. The goal is to develop an intelligent
cruise control in order to extend the vehicle range, i.e. to minimize energy consumption,
by computing the optimal torque profile for a given track. On the one hand, a
path-based linear model with strong simplifications regarding the vehicle dynamics
is used. On the other hand, a nonlinear model is employed in which the dynamics
of the mechanical and electrical subsystem are modeled.
author:
- first_name: Julian
full_name: Eckstein, Julian
last_name: Eckstein
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Kai
full_name: Schäfer, Kai
last_name: Schäfer
- first_name: Patrick
full_name: Friedel, Patrick
last_name: Friedel
- first_name: Ulrich
full_name: Köhler, Ulrich
last_name: Köhler
- first_name: 'Mirko '
full_name: 'Hessel von Molo, Mirko '
last_name: Hessel von Molo
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Eckstein J, Peitz S, Schäfer K, et al. A comparison of two predictive approaches
to control the longitudinal dynamics of electric vehicles. In: Procedia Technology,
3rd International Conference on System-Integrated Intelligence: New Challenges
for Product and Production Engineering. Vol 26. ; 2016:465-472. doi:10.1016/j.protcy.2016.08.059'
apa: 'Eckstein, J., Peitz, S., Schäfer, K., Friedel, P., Köhler, U., Hessel von
Molo, M., Ober-Blöbaum, S., & Dellnitz, M. (2016). A comparison of two predictive
approaches to control the longitudinal dynamics of electric vehicles. Procedia
Technology, 3rd International Conference on System-Integrated Intelligence: New
Challenges for Product and Production Engineering, 26, 465–472. https://doi.org/10.1016/j.protcy.2016.08.059'
bibtex: '@inproceedings{Eckstein_Peitz_Schäfer_Friedel_Köhler_Hessel von Molo_Ober-Blöbaum_Dellnitz_2016,
title={A comparison of two predictive approaches to control the longitudinal dynamics
of electric vehicles}, volume={26}, DOI={10.1016/j.protcy.2016.08.059},
booktitle={Procedia Technology, 3rd International Conference on System-Integrated
Intelligence: New Challenges for Product and Production Engineering}, author={Eckstein,
Julian and Peitz, Sebastian and Schäfer, Kai and Friedel, Patrick and Köhler,
Ulrich and Hessel von Molo, Mirko and Ober-Blöbaum, Sina and Dellnitz, Michael},
year={2016}, pages={465–472} }'
chicago: 'Eckstein, Julian, Sebastian Peitz, Kai Schäfer, Patrick Friedel, Ulrich
Köhler, Mirko Hessel von Molo, Sina Ober-Blöbaum, and Michael Dellnitz. “A Comparison
of Two Predictive Approaches to Control the Longitudinal Dynamics of Electric
Vehicles.” In Procedia Technology, 3rd International Conference on System-Integrated
Intelligence: New Challenges for Product and Production Engineering, 26:465–72,
2016. https://doi.org/10.1016/j.protcy.2016.08.059.'
ieee: 'J. Eckstein et al., “A comparison of two predictive approaches to
control the longitudinal dynamics of electric vehicles,” in Procedia Technology,
3rd International Conference on System-Integrated Intelligence: New Challenges
for Product and Production Engineering, 2016, vol. 26, pp. 465–472, doi: 10.1016/j.protcy.2016.08.059.'
mla: 'Eckstein, Julian, et al. “A Comparison of Two Predictive Approaches to Control
the Longitudinal Dynamics of Electric Vehicles.” Procedia Technology, 3rd International
Conference on System-Integrated Intelligence: New Challenges for Product and Production
Engineering, vol. 26, 2016, pp. 465–72, doi:10.1016/j.protcy.2016.08.059.'
short: 'J. Eckstein, S. Peitz, K. Schäfer, P. Friedel, U. Köhler, M. Hessel von
Molo, S. Ober-Blöbaum, M. Dellnitz, in: Procedia Technology, 3rd International
Conference on System-Integrated Intelligence: New Challenges for Product and Production
Engineering, 2016, pp. 465–472.'
date_created: 2019-03-29T13:35:25Z
date_updated: 2022-01-21T14:10:10Z
department:
- _id: '101'
doi: 10.1016/j.protcy.2016.08.059
intvolume: ' 26'
language:
- iso: eng
page: 465-472
publication: 'Procedia Technology, 3rd International Conference on System-Integrated
Intelligence: New Challenges for Product and Production Engineering'
publication_identifier:
issn:
- 2212-0173
publication_status: published
status: public
title: A comparison of two predictive approaches to control the longitudinal dynamics
of electric vehicles
type: conference
user_id: '15694'
volume: 26
year: '2016'
...
---
_id: '16553'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Stefan
full_name: Sertl, Stefan
last_name: Sertl
citation:
ama: 'Dellnitz M, Froyland G, Sertl S. A Conjecture on the Existence of Isolated
Eigenvalues of the Perron-Frobenius Operator. In: Equadiff 99. ; 2000.
doi:10.1142/9789812792617_0199'
apa: Dellnitz, M., Froyland, G., & Sertl, S. (2000). A Conjecture on the Existence
of Isolated Eigenvalues of the Perron-Frobenius Operator. In Equadiff 99.
https://doi.org/10.1142/9789812792617_0199
bibtex: '@inbook{Dellnitz_Froyland_Sertl_2000, title={A Conjecture on the Existence
of Isolated Eigenvalues of the Perron-Frobenius Operator}, DOI={10.1142/9789812792617_0199},
booktitle={Equadiff 99}, author={Dellnitz, Michael and Froyland, Gary and Sertl,
Stefan}, year={2000} }'
chicago: Dellnitz, Michael, Gary Froyland, and Stefan Sertl. “A Conjecture on the
Existence of Isolated Eigenvalues of the Perron-Frobenius Operator.” In Equadiff
99, 2000. https://doi.org/10.1142/9789812792617_0199.
ieee: M. Dellnitz, G. Froyland, and S. Sertl, “A Conjecture on the Existence of
Isolated Eigenvalues of the Perron-Frobenius Operator,” in Equadiff 99,
2000.
mla: Dellnitz, Michael, et al. “A Conjecture on the Existence of Isolated Eigenvalues
of the Perron-Frobenius Operator.” Equadiff 99, 2000, doi:10.1142/9789812792617_0199.
short: 'M. Dellnitz, G. Froyland, S. Sertl, in: Equadiff 99, 2000.'
date_created: 2020-04-15T09:08:34Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1142/9789812792617_0199
language:
- iso: eng
publication: Equadiff 99
publication_identifier:
isbn:
- '9789810243593'
- '9789812792617'
publication_status: published
status: public
title: A Conjecture on the Existence of Isolated Eigenvalues of the Perron-Frobenius
Operator
type: book_chapter
user_id: '15701'
year: '2000'
...
---
_id: '8750'
abstract:
- lang: eng
text: In this article we propose a descent method for equality and inequality constrained
multiobjective optimization problems (MOPs) which generalizes the steepest descent
method for unconstrained MOPs by Fliege and Svaiter to constrained problems by
using two active set strategies. Under some regularity assumptions on the problem,
we show that accumulation points of our descent method satisfy a necessary condition
for local Pareto optimality. Finally, we show the typical behavior of our method
in a numerical example.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Gebken B, Peitz S, Dellnitz M. A Descent Method for Equality and Inequality
Constrained Multiobjective Optimization Problems. In: Numerical and Evolutionary
Optimization – NEO 2017. Cham; 2018. doi:10.1007/978-3-319-96104-0_2'
apa: Gebken, B., Peitz, S., & Dellnitz, M. (2018). A Descent Method for Equality
and Inequality Constrained Multiobjective Optimization Problems. In Numerical
and Evolutionary Optimization – NEO 2017. Cham. https://doi.org/10.1007/978-3-319-96104-0_2
bibtex: '@inproceedings{Gebken_Peitz_Dellnitz_2018, place={Cham}, title={A Descent
Method for Equality and Inequality Constrained Multiobjective Optimization Problems},
DOI={10.1007/978-3-319-96104-0_2},
booktitle={Numerical and Evolutionary Optimization – NEO 2017}, author={Gebken,
Bennet and Peitz, Sebastian and Dellnitz, Michael}, year={2018} }'
chicago: Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “A Descent Method
for Equality and Inequality Constrained Multiobjective Optimization Problems.”
In Numerical and Evolutionary Optimization – NEO 2017. Cham, 2018. https://doi.org/10.1007/978-3-319-96104-0_2.
ieee: B. Gebken, S. Peitz, and M. Dellnitz, “A Descent Method for Equality and Inequality
Constrained Multiobjective Optimization Problems,” in Numerical and Evolutionary
Optimization – NEO 2017, 2018.
mla: Gebken, Bennet, et al. “A Descent Method for Equality and Inequality Constrained
Multiobjective Optimization Problems.” Numerical and Evolutionary Optimization
– NEO 2017, 2018, doi:10.1007/978-3-319-96104-0_2.
short: 'B. Gebken, S. Peitz, M. Dellnitz, in: Numerical and Evolutionary Optimization
– NEO 2017, Cham, 2018.'
conference:
name: 'NEO 2017: Numerical and Evolutionary Optimization'
date_created: 2019-03-29T13:26:47Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.1007/978-3-319-96104-0_2
language:
- iso: eng
place: Cham
publication: Numerical and Evolutionary Optimization – NEO 2017
publication_identifier:
isbn:
- '9783319961033'
- '9783319961040'
issn:
- 1860-949X
- 1860-9503
publication_status: published
status: public
title: A Descent Method for Equality and Inequality Constrained Multiobjective Optimization
Problems
type: conference
user_id: '47427'
year: '2018'
...
---
_id: '51334'
abstract:
- lang: eng
text: The efficient optimization method for locally Lipschitz continuous multiobjective
optimization problems from [1] is extended from finite-dimensional problems to
general Hilbert spaces. The method iteratively computes Pareto critical points,
where in each iteration, an approximation of the subdifferential is computed in
an efficient manner and then used to compute a common descent direction for all
objective functions. To prove convergence, we present some new optimality results
for nonsmooth multiobjective optimization problems in Hilbert spaces. Using these,
we can show that every accumulation point of the sequence generated by our algorithm
is Pareto critical under common assumptions. Computational efficiency for finding
Pareto critical points is numerically demonstrated for multiobjective optimal
control of an obstacle problem.
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Georg
full_name: Müller, Georg
last_name: Müller
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: Sonntag K, Gebken B, Müller G, Peitz S, Volkwein S. A Descent Method for Nonsmooth
Multiobjective Optimization in Hilbert Spaces. arXiv:240206376. Published
online 2024.
apa: Sonntag, K., Gebken, B., Müller, G., Peitz, S., & Volkwein, S. (2024).
A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces.
In arXiv:2402.06376.
bibtex: '@article{Sonntag_Gebken_Müller_Peitz_Volkwein_2024, title={A Descent Method
for Nonsmooth Multiobjective Optimization in Hilbert Spaces}, journal={arXiv:2402.06376},
author={Sonntag, Konstantin and Gebken, Bennet and Müller, Georg and Peitz, Sebastian
and Volkwein, Stefan}, year={2024} }'
chicago: Sonntag, Konstantin, Bennet Gebken, Georg Müller, Sebastian Peitz, and
Stefan Volkwein. “A Descent Method for Nonsmooth Multiobjective Optimization in
Hilbert Spaces.” ArXiv:2402.06376, 2024.
ieee: K. Sonntag, B. Gebken, G. Müller, S. Peitz, and S. Volkwein, “A Descent Method
for Nonsmooth Multiobjective Optimization in Hilbert Spaces,” arXiv:2402.06376.
2024.
mla: Sonntag, Konstantin, et al. “A Descent Method for Nonsmooth Multiobjective
Optimization in Hilbert Spaces.” ArXiv:2402.06376, 2024.
short: K. Sonntag, B. Gebken, G. Müller, S. Peitz, S. Volkwein, ArXiv:2402.06376
(2024).
date_created: 2024-02-13T09:35:26Z
date_updated: 2024-02-21T10:21:03Z
department:
- _id: '101'
- _id: '655'
external_id:
arxiv:
- "\t2402.06376"
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2402.06376
oa: '1'
publication: arXiv:2402.06376
status: public
title: A Descent Method for Nonsmooth Multiobjective Optimization in Hilbert Spaces
type: preprint
user_id: '56399'
year: '2024'
...
---
_id: '16666'
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: El-ghazali
full_name: Talbi, El-ghazali
last_name: Talbi
- first_name: Gregorio Toscano
full_name: Pulido, Gregorio Toscano
last_name: Pulido
- first_name: Carlos Coello
full_name: Coello, Carlos Coello
last_name: Coello
- first_name: Luis Vicente
full_name: Santana-Quintero, Luis Vicente
last_name: Santana-Quintero
citation:
ama: 'Schütze O, Talbi E, Pulido GT, Coello CC, Santana-Quintero LV. A Memetic PSO
Algorithm for Scalar Optimization Problems. In: 2007 IEEE Swarm Intelligence
Symposium. ; 2007. doi:10.1109/sis.2007.368036'
apa: Schütze, O., Talbi, E., Pulido, G. T., Coello, C. C., & Santana-Quintero,
L. V. (2007). A Memetic PSO Algorithm for Scalar Optimization Problems. In 2007
IEEE Swarm Intelligence Symposium. https://doi.org/10.1109/sis.2007.368036
bibtex: '@inproceedings{Schütze_Talbi_Pulido_Coello_Santana-Quintero_2007, title={A
Memetic PSO Algorithm for Scalar Optimization Problems}, DOI={10.1109/sis.2007.368036},
booktitle={2007 IEEE Swarm Intelligence Symposium}, author={Schütze, Oliver and
Talbi, El-ghazali and Pulido, Gregorio Toscano and Coello, Carlos Coello and Santana-Quintero,
Luis Vicente}, year={2007} }'
chicago: Schütze, Oliver, El-ghazali Talbi, Gregorio Toscano Pulido, Carlos Coello
Coello, and Luis Vicente Santana-Quintero. “A Memetic PSO Algorithm for Scalar
Optimization Problems.” In 2007 IEEE Swarm Intelligence Symposium, 2007.
https://doi.org/10.1109/sis.2007.368036.
ieee: O. Schütze, E. Talbi, G. T. Pulido, C. C. Coello, and L. V. Santana-Quintero,
“A Memetic PSO Algorithm for Scalar Optimization Problems,” in 2007 IEEE Swarm
Intelligence Symposium, 2007.
mla: Schütze, Oliver, et al. “A Memetic PSO Algorithm for Scalar Optimization Problems.”
2007 IEEE Swarm Intelligence Symposium, 2007, doi:10.1109/sis.2007.368036.
short: 'O. Schütze, E. Talbi, G.T. Pulido, C.C. Coello, L.V. Santana-Quintero, in:
2007 IEEE Swarm Intelligence Symposium, 2007.'
date_created: 2020-04-16T10:00:10Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1109/sis.2007.368036
language:
- iso: eng
publication: 2007 IEEE Swarm Intelligence Symposium
publication_identifier:
isbn:
- '1424407087'
publication_status: published
status: public
title: A Memetic PSO Algorithm for Scalar Optimization Problems
type: conference
user_id: '15701'
year: '2007'
...
---
_id: '16574'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Marcus
full_name: Post, Marcus
last_name: Post
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Bianca
full_name: Thiere, Bianca
last_name: Thiere
citation:
ama: Dellnitz M, Ober-Blöbaum S, Post M, Schütze O, Thiere B. A multi-objective
approach to the design of low thrust space trajectories using optimal control.
Celestial Mechanics and Dynamical Astronomy. 2009:33-59. doi:10.1007/s10569-009-9229-y
apa: Dellnitz, M., Ober-Blöbaum, S., Post, M., Schütze, O., & Thiere, B. (2009).
A multi-objective approach to the design of low thrust space trajectories using
optimal control. Celestial Mechanics and Dynamical Astronomy, 33–59. https://doi.org/10.1007/s10569-009-9229-y
bibtex: '@article{Dellnitz_Ober-Blöbaum_Post_Schütze_Thiere_2009, title={A multi-objective
approach to the design of low thrust space trajectories using optimal control},
DOI={10.1007/s10569-009-9229-y},
journal={Celestial Mechanics and Dynamical Astronomy}, author={Dellnitz, Michael
and Ober-Blöbaum, Sina and Post, Marcus and Schütze, Oliver and Thiere, Bianca},
year={2009}, pages={33–59} }'
chicago: Dellnitz, Michael, Sina Ober-Blöbaum, Marcus Post, Oliver Schütze, and
Bianca Thiere. “A Multi-Objective Approach to the Design of Low Thrust Space Trajectories
Using Optimal Control.” Celestial Mechanics and Dynamical Astronomy, 2009,
33–59. https://doi.org/10.1007/s10569-009-9229-y.
ieee: M. Dellnitz, S. Ober-Blöbaum, M. Post, O. Schütze, and B. Thiere, “A multi-objective
approach to the design of low thrust space trajectories using optimal control,”
Celestial Mechanics and Dynamical Astronomy, pp. 33–59, 2009.
mla: Dellnitz, Michael, et al. “A Multi-Objective Approach to the Design of Low
Thrust Space Trajectories Using Optimal Control.” Celestial Mechanics and Dynamical
Astronomy, 2009, pp. 33–59, doi:10.1007/s10569-009-9229-y.
short: M. Dellnitz, S. Ober-Blöbaum, M. Post, O. Schütze, B. Thiere, Celestial Mechanics
and Dynamical Astronomy (2009) 33–59.
date_created: 2020-04-16T05:05:17Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/s10569-009-9229-y
language:
- iso: eng
page: 33-59
publication: Celestial Mechanics and Dynamical Astronomy
publication_identifier:
issn:
- 0923-2958
- 1572-9478
publication_status: published
status: public
title: A multi-objective approach to the design of low thrust space trajectories using
optimal control
type: journal_article
user_id: '15701'
year: '2009'
...
---
_id: '8756'
abstract:
- lang: eng
text: We present a new algorithm for model predictive control of non-linear systems
with respect to multiple, conflicting objectives. The idea is to provide a possibility
to change the objective in real-time, e.g. as a reaction to changes in the environment
or the system state itself. The algorithm utilises elements from various well-established
concepts, namely multiobjective optimal control, economic as well as explicit
model predictive control and motion planning with motion primitives. In order
to realise real-time applicability, we split the computation into an online and
an offline phase and we utilise symmetries in the open-loop optimal control problem
to reduce the number of multiobjective optimal control problems that need to be
solved in the offline phase. The results are illustrated using the example of
an electric vehicle where the longitudinal dynamics are controlled with respect
to the concurrent objectives arrival time and energy consumption.
article_type: original
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Kai
full_name: Schäfer, Kai
last_name: Schäfer
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Julian
full_name: Eckstein, Julian
last_name: Eckstein
- first_name: Ulrich
full_name: Köhler, Ulrich
last_name: Köhler
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Peitz S, Schäfer K, Ober-Blöbaum S, Eckstein J, Köhler U, Dellnitz M. A multiobjective
MPC approach for autonomously driven electric vehicles. Proceedings of the
20th World Congress of the International Federation of Automatic Control (IFAC).
2017;50(1):8674-8679. doi:10.1016/j.ifacol.2017.08.1526
apa: Peitz, S., Schäfer, K., Ober-Blöbaum, S., Eckstein, J., Köhler, U., & Dellnitz,
M. (2017). A multiobjective MPC approach for autonomously driven electric vehicles.
Proceedings of the 20th World Congress of the International Federation of Automatic
Control (IFAC), 50(1), 8674–8679. https://doi.org/10.1016/j.ifacol.2017.08.1526
bibtex: '@article{Peitz_Schäfer_Ober-Blöbaum_Eckstein_Köhler_Dellnitz_2017, title={A
multiobjective MPC approach for autonomously driven electric vehicles}, volume={50},
DOI={10.1016/j.ifacol.2017.08.1526},
number={1}, journal={Proceedings of the 20th World Congress of the International
Federation of Automatic Control (IFAC)}, author={Peitz, Sebastian and Schäfer,
Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz,
Michael}, year={2017}, pages={8674–8679} }'
chicago: 'Peitz, Sebastian, Kai Schäfer, Sina Ober-Blöbaum, Julian Eckstein, Ulrich
Köhler, and Michael Dellnitz. “A Multiobjective MPC Approach for Autonomously
Driven Electric Vehicles.” Proceedings of the 20th World Congress of the International
Federation of Automatic Control (IFAC) 50, no. 1 (2017): 8674–79. https://doi.org/10.1016/j.ifacol.2017.08.1526.'
ieee: 'S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, and M. Dellnitz,
“A multiobjective MPC approach for autonomously driven electric vehicles,” Proceedings
of the 20th World Congress of the International Federation of Automatic Control
(IFAC), vol. 50, no. 1, pp. 8674–8679, 2017, doi: 10.1016/j.ifacol.2017.08.1526.'
mla: Peitz, Sebastian, et al. “A Multiobjective MPC Approach for Autonomously Driven
Electric Vehicles.” Proceedings of the 20th World Congress of the International
Federation of Automatic Control (IFAC), vol. 50, no. 1, 2017, pp. 8674–79,
doi:10.1016/j.ifacol.2017.08.1526.
short: S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, M. Dellnitz,
Proceedings of the 20th World Congress of the International Federation of Automatic
Control (IFAC) 50 (2017) 8674–8679.
conference:
end_date: 2017-07-14
start_date: 2017-07-09
date_created: 2019-03-29T13:32:46Z
date_updated: 2022-01-21T13:58:41Z
department:
- _id: '101'
doi: 10.1016/j.ifacol.2017.08.1526
intvolume: ' 50'
issue: '1'
language:
- iso: eng
page: 8674-8679
publication: Proceedings of the 20th World Congress of the International Federation
of Automatic Control (IFAC)
publication_identifier:
issn:
- 2405-8963
publication_status: published
status: public
title: A multiobjective MPC approach for autonomously driven electric vehicles
type: journal_article
user_id: '15694'
volume: 50
year: '2017'
...
---
_id: '16657'
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
last_name: Peitz
- first_name: Kai
full_name: Schäfer, Kai
last_name: Schäfer
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Julian
full_name: Eckstein, Julian
last_name: Eckstein
- first_name: Ulrich
full_name: Köhler, Ulrich
last_name: Köhler
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Peitz S, Schäfer K, Ober-Blöbaum S, Eckstein J, Köhler U, Dellnitz M. A Multiobjective
MPC Approach for Autonomously Driven Electric Vehicles * *This research was funded
by the German Federal Ministry of Education and Research (BMBF) within the Leading-Edge
Cluster Intelligent Technical Systems OstWestfalenLippe (it’s OWL). IFAC-PapersOnLine.
2017:8674-8679. doi:10.1016/j.ifacol.2017.08.1526
apa: Peitz, S., Schäfer, K., Ober-Blöbaum, S., Eckstein, J., Köhler, U., & Dellnitz,
M. (2017). A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles
* *This research was funded by the German Federal Ministry of Education and Research
(BMBF) within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe
(it’s OWL). IFAC-PapersOnLine, 8674–8679. https://doi.org/10.1016/j.ifacol.2017.08.1526
bibtex: '@article{Peitz_Schäfer_Ober-Blöbaum_Eckstein_Köhler_Dellnitz_2017, title={A
Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This
research was funded by the German Federal Ministry of Education and Research (BMBF)
within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe
(it’s OWL).}, DOI={10.1016/j.ifacol.2017.08.1526},
journal={IFAC-PapersOnLine}, author={Peitz, Sebastian and Schäfer, Kai and Ober-Blöbaum,
Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz, Michael}, year={2017},
pages={8674–8679} }'
chicago: Peitz, Sebastian, Kai Schäfer, Sina Ober-Blöbaum, Julian Eckstein, Ulrich
Köhler, and Michael Dellnitz. “A Multiobjective MPC Approach for Autonomously
Driven Electric Vehicles * *This Research Was Funded by the German Federal Ministry
of Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical
Systems OstWestfalenLippe (It’s OWL).” IFAC-PapersOnLine, 2017, 8674–79.
https://doi.org/10.1016/j.ifacol.2017.08.1526.
ieee: S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, and M. Dellnitz,
“A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This
research was funded by the German Federal Ministry of Education and Research (BMBF)
within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe
(it’s OWL).,” IFAC-PapersOnLine, pp. 8674–8679, 2017.
mla: Peitz, Sebastian, et al. “A Multiobjective MPC Approach for Autonomously Driven
Electric Vehicles * *This Research Was Funded by the German Federal Ministry of
Education and Research (BMBF) within the Leading-Edge Cluster Intelligent Technical
Systems OstWestfalenLippe (It’s OWL).” IFAC-PapersOnLine, 2017, pp. 8674–79,
doi:10.1016/j.ifacol.2017.08.1526.
short: S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, M. Dellnitz,
IFAC-PapersOnLine (2017) 8674–8679.
date_created: 2020-04-16T09:30:56Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1016/j.ifacol.2017.08.1526
language:
- iso: eng
page: 8674-8679
publication: IFAC-PapersOnLine
publication_identifier:
issn:
- 2405-8963
publication_status: published
status: public
title: A Multiobjective MPC Approach for Autonomously Driven Electric Vehicles * *This
research was funded by the German Federal Ministry of Education and Research (BMBF)
within the Leading-Edge Cluster Intelligent Technical Systems OstWestfalenLippe
(it’s OWL).
type: journal_article
user_id: '15701'
year: '2017'
...
---
_id: '16643'
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Albert
full_name: Seifried, Albert
last_name: Seifried
citation:
ama: 'Ober-Blöbaum S, Seifried A. A multiobjective optimization approach for optimal
control problems of mechanical systems with uncertainties. In: 2013 European
Control Conference (ECC). ; 2013. doi:10.23919/ecc.2013.6669594'
apa: Ober-Blöbaum, S., & Seifried, A. (2013). A multiobjective optimization
approach for optimal control problems of mechanical systems with uncertainties.
In 2013 European Control Conference (ECC). https://doi.org/10.23919/ecc.2013.6669594
bibtex: '@inproceedings{Ober-Blöbaum_Seifried_2013, title={A multiobjective optimization
approach for optimal control problems of mechanical systems with uncertainties},
DOI={10.23919/ecc.2013.6669594},
booktitle={2013 European Control Conference (ECC)}, author={Ober-Blöbaum, Sina
and Seifried, Albert}, year={2013} }'
chicago: Ober-Blöbaum, Sina, and Albert Seifried. “A Multiobjective Optimization
Approach for Optimal Control Problems of Mechanical Systems with Uncertainties.”
In 2013 European Control Conference (ECC), 2013. https://doi.org/10.23919/ecc.2013.6669594.
ieee: S. Ober-Blöbaum and A. Seifried, “A multiobjective optimization approach for
optimal control problems of mechanical systems with uncertainties,” in 2013
European Control Conference (ECC), 2013.
mla: Ober-Blöbaum, Sina, and Albert Seifried. “A Multiobjective Optimization Approach
for Optimal Control Problems of Mechanical Systems with Uncertainties.” 2013
European Control Conference (ECC), 2013, doi:10.23919/ecc.2013.6669594.
short: 'S. Ober-Blöbaum, A. Seifried, in: 2013 European Control Conference (ECC),
2013.'
date_created: 2020-04-16T09:01:37Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.23919/ecc.2013.6669594
language:
- iso: eng
publication: 2013 European Control Conference (ECC)
publication_identifier:
isbn:
- '9783033039629'
publication_status: published
status: public
title: A multiobjective optimization approach for optimal control problems of mechanical
systems with uncertainties
type: conference
user_id: '15701'
year: '2013'
...
---
_id: '16678'
author:
- first_name: Katrin
full_name: Witting, Katrin
last_name: Witting
- first_name: Bernd
full_name: Schulz, Bernd
last_name: Schulz
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Joachim
full_name: Böcker, Joachim
last_name: Böcker
- first_name: Norbert
full_name: Fröhleke, Norbert
last_name: Fröhleke
citation:
ama: Witting K, Schulz B, Dellnitz M, Böcker J, Fröhleke N. A new approach for online
multiobjective optimization of mechatronic systems. International Journal on
Software Tools for Technology Transfer. 2008:223-231. doi:10.1007/s10009-008-0066-1
apa: Witting, K., Schulz, B., Dellnitz, M., Böcker, J., & Fröhleke, N. (2008).
A new approach for online multiobjective optimization of mechatronic systems.
International Journal on Software Tools for Technology Transfer, 223–231.
https://doi.org/10.1007/s10009-008-0066-1
bibtex: '@article{Witting_Schulz_Dellnitz_Böcker_Fröhleke_2008, title={A new approach
for online multiobjective optimization of mechatronic systems}, DOI={10.1007/s10009-008-0066-1},
journal={International Journal on Software Tools for Technology Transfer}, author={Witting,
Katrin and Schulz, Bernd and Dellnitz, Michael and Böcker, Joachim and Fröhleke,
Norbert}, year={2008}, pages={223–231} }'
chicago: Witting, Katrin, Bernd Schulz, Michael Dellnitz, Joachim Böcker, and Norbert
Fröhleke. “A New Approach for Online Multiobjective Optimization of Mechatronic
Systems.” International Journal on Software Tools for Technology Transfer,
2008, 223–31. https://doi.org/10.1007/s10009-008-0066-1.
ieee: K. Witting, B. Schulz, M. Dellnitz, J. Böcker, and N. Fröhleke, “A new approach
for online multiobjective optimization of mechatronic systems,” International
Journal on Software Tools for Technology Transfer, pp. 223–231, 2008.
mla: Witting, Katrin, et al. “A New Approach for Online Multiobjective Optimization
of Mechatronic Systems.” International Journal on Software Tools for Technology
Transfer, 2008, pp. 223–31, doi:10.1007/s10009-008-0066-1.
short: K. Witting, B. Schulz, M. Dellnitz, J. Böcker, N. Fröhleke, International
Journal on Software Tools for Technology Transfer (2008) 223–231.
date_created: 2020-04-16T10:22:02Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/s10009-008-0066-1
language:
- iso: eng
page: 223-231
publication: International Journal on Software Tools for Technology Transfer
publication_identifier:
issn:
- 1433-2779
- 1433-2787
publication_status: published
status: public
title: A new approach for online multiobjective optimization of mechatronic systems
type: journal_article
user_id: '15701'
year: '2008'
...
---
_id: '16664'
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
citation:
ama: 'Schütze O. A New Data Structure for the Nondominance Problem in Multi-objective
Optimization. In: Lecture Notes in Computer Science. Berlin, Heidelberg;
2003. doi:10.1007/3-540-36970-8_36'
apa: Schütze, O. (2003). A New Data Structure for the Nondominance Problem in Multi-objective
Optimization. In Lecture Notes in Computer Science. Berlin, Heidelberg.
https://doi.org/10.1007/3-540-36970-8_36
bibtex: '@inbook{Schütze_2003, place={Berlin, Heidelberg}, title={A New Data Structure
for the Nondominance Problem in Multi-objective Optimization}, DOI={10.1007/3-540-36970-8_36},
booktitle={Lecture Notes in Computer Science}, author={Schütze, Oliver}, year={2003}
}'
chicago: Schütze, Oliver. “A New Data Structure for the Nondominance Problem in
Multi-Objective Optimization.” In Lecture Notes in Computer Science. Berlin,
Heidelberg, 2003. https://doi.org/10.1007/3-540-36970-8_36.
ieee: O. Schütze, “A New Data Structure for the Nondominance Problem in Multi-objective
Optimization,” in Lecture Notes in Computer Science, Berlin, Heidelberg,
2003.
mla: Schütze, Oliver. “A New Data Structure for the Nondominance Problem in Multi-Objective
Optimization.” Lecture Notes in Computer Science, 2003, doi:10.1007/3-540-36970-8_36.
short: 'O. Schütze, in: Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.'
date_created: 2020-04-16T09:57:05Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/3-540-36970-8_36
language:
- iso: eng
place: Berlin, Heidelberg
publication: Lecture Notes in Computer Science
publication_identifier:
isbn:
- '9783540018698'
- '9783540369707'
issn:
- 0302-9743
publication_status: published
status: public
title: A New Data Structure for the Nondominance Problem in Multi-objective Optimization
type: book_chapter
user_id: '15701'
year: '2003'
...
---
_id: '51208'
abstract:
- lang: eng
text: AbstractApproximation of subdifferentials
is one of the main tasks when computing descent directions for nonsmooth optimization
problems. In this article, we propose a bisection method for weakly lower semismooth
functions which is able to compute new subgradients that improve a given approximation
in case a direction with insufficient descent was computed. Combined with a recently
proposed deterministic gradient sampling approach, this yields a deterministic
and provably convergent way to approximate subdifferentials for computing descent
directions.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. A note on the convergence of deterministic gradient sampling in nonsmooth
optimization. Computational Optimization and Applications. Published online
2024. doi:10.1007/s10589-024-00552-0
apa: Gebken, B. (2024). A note on the convergence of deterministic gradient sampling
in nonsmooth optimization. Computational Optimization and Applications.
https://doi.org/10.1007/s10589-024-00552-0
bibtex: '@article{Gebken_2024, title={A note on the convergence of deterministic
gradient sampling in nonsmooth optimization}, DOI={10.1007/s10589-024-00552-0},
journal={Computational Optimization and Applications}, publisher={Springer Science
and Business Media LLC}, author={Gebken, Bennet}, year={2024} }'
chicago: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
2024. https://doi.org/10.1007/s10589-024-00552-0.
ieee: 'B. Gebken, “A note on the convergence of deterministic gradient sampling
in nonsmooth optimization,” Computational Optimization and Applications,
2024, doi: 10.1007/s10589-024-00552-0.'
mla: Gebken, Bennet. “A Note on the Convergence of Deterministic Gradient Sampling
in Nonsmooth Optimization.” Computational Optimization and Applications,
Springer Science and Business Media LLC, 2024, doi:10.1007/s10589-024-00552-0.
short: B. Gebken, Computational Optimization and Applications (2024).
date_created: 2024-02-07T07:23:23Z
date_updated: 2024-02-08T08:05:54Z
department:
- _id: '101'
doi: 10.1007/s10589-024-00552-0
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
language:
- iso: eng
publication: Computational Optimization and Applications
publication_identifier:
issn:
- 0926-6003
- 1573-2894
publication_status: published
publisher: Springer Science and Business Media LLC
status: public
title: A note on the convergence of deterministic gradient sampling in nonsmooth optimization
type: journal_article
user_id: '32643'
year: '2024'
...
---
_id: '16542'
author:
- first_name: M
full_name: Dellnitz, M
last_name: Dellnitz
- first_name: I
full_name: Melbourne, I
last_name: Melbourne
citation:
ama: Dellnitz M, Melbourne I. A note on the shadowing lemma and symmetric periodic
points. Nonlinearity. 1995:1067-1075. doi:10.1088/0951-7715/8/6/010
apa: Dellnitz, M., & Melbourne, I. (1995). A note on the shadowing lemma and
symmetric periodic points. Nonlinearity, 1067–1075. https://doi.org/10.1088/0951-7715/8/6/010
bibtex: '@article{Dellnitz_Melbourne_1995, title={A note on the shadowing lemma
and symmetric periodic points}, DOI={10.1088/0951-7715/8/6/010},
journal={Nonlinearity}, author={Dellnitz, M and Melbourne, I}, year={1995}, pages={1067–1075}
}'
chicago: Dellnitz, M, and I Melbourne. “A Note on the Shadowing Lemma and Symmetric
Periodic Points.” Nonlinearity, 1995, 1067–75. https://doi.org/10.1088/0951-7715/8/6/010.
ieee: M. Dellnitz and I. Melbourne, “A note on the shadowing lemma and symmetric
periodic points,” Nonlinearity, pp. 1067–1075, 1995.
mla: Dellnitz, M., and I. Melbourne. “A Note on the Shadowing Lemma and Symmetric
Periodic Points.” Nonlinearity, 1995, pp. 1067–75, doi:10.1088/0951-7715/8/6/010.
short: M. Dellnitz, I. Melbourne, Nonlinearity (1995) 1067–1075.
date_created: 2020-04-15T08:46:30Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1088/0951-7715/8/6/010
language:
- iso: eng
page: 1067-1075
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: A note on the shadowing lemma and symmetric periodic points
type: journal_article
user_id: '15701'
year: '1995'
...
---
_id: '45498'
abstract:
- lang: eng
text: "We present a novel method for high-order phase reduction in networks of\r\nweakly
coupled oscillators and, more generally, perturbations of reducible\r\nnormally
hyperbolic (quasi-)periodic tori. Our method works by computing an\r\nasymptotic
expansion for an embedding of the perturbed invariant torus, as well\r\nas for
the reduced phase dynamics in local coordinates. Both can be determined\r\nto
arbitrary degrees of accuracy, and we show that the phase dynamics may\r\ndirectly
be obtained in normal form. We apply the method to predict remote\r\nsynchronisation
in a chain of coupled Stuart-Landau oscillators."
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
citation:
ama: von der Gracht S, Nijholt E, Rink B. A parametrisation method for high-order
phase reduction in coupled oscillator networks. arXiv:230603320.
apa: von der Gracht, S., Nijholt, E., & Rink, B. (n.d.). A parametrisation method
for high-order phase reduction in coupled oscillator networks. In arXiv:2306.03320.
bibtex: '@article{von der Gracht_Nijholt_Rink, title={A parametrisation method for
high-order phase reduction in coupled oscillator networks}, journal={arXiv:2306.03320},
author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob} }'
chicago: Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “A Parametrisation
Method for High-Order Phase Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320,
n.d.
ieee: S. von der Gracht, E. Nijholt, and B. Rink, “A parametrisation method for
high-order phase reduction in coupled oscillator networks,” arXiv:2306.03320.
.
mla: von der Gracht, Sören, et al. “A Parametrisation Method for High-Order Phase
Reduction in Coupled Oscillator Networks.” ArXiv:2306.03320.
short: S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2306.03320 (n.d.).
date_created: 2023-06-07T07:57:28Z
date_updated: 2023-06-07T07:59:06Z
department:
- _id: '101'
external_id:
arxiv:
- '2306.03320'
language:
- iso: eng
main_file_link:
- url: https://arxiv.org/pdf/2306.03320
page: '29'
publication: arXiv:2306.03320
publication_status: submitted
status: public
title: A parametrisation method for high-order phase reduction in coupled oscillator
networks
type: preprint
user_id: '97359'
year: '2023'
...
---
_id: '16527'
author:
- first_name: S.
full_name: Day, S.
last_name: Day
- first_name: O.
full_name: Junge, O.
last_name: Junge
- first_name: K.
full_name: Mischaikow, K.
last_name: Mischaikow
citation:
ama: Day S, Junge O, Mischaikow K. A Rigorous Numerical Method for the Global Analysis
of Infinite-Dimensional Discrete Dynamical Systems. SIAM Journal on Applied
Dynamical Systems. 2004:117-160. doi:10.1137/030600210
apa: Day, S., Junge, O., & Mischaikow, K. (2004). A Rigorous Numerical Method
for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems. SIAM
Journal on Applied Dynamical Systems, 117–160. https://doi.org/10.1137/030600210
bibtex: '@article{Day_Junge_Mischaikow_2004, title={A Rigorous Numerical Method
for the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems}, DOI={10.1137/030600210}, journal={SIAM
Journal on Applied Dynamical Systems}, author={Day, S. and Junge, O. and Mischaikow,
K.}, year={2004}, pages={117–160} }'
chicago: Day, S., O. Junge, and K. Mischaikow. “A Rigorous Numerical Method for
the Global Analysis of Infinite-Dimensional Discrete Dynamical Systems.” SIAM
Journal on Applied Dynamical Systems, 2004, 117–60. https://doi.org/10.1137/030600210.
ieee: S. Day, O. Junge, and K. Mischaikow, “A Rigorous Numerical Method for the
Global Analysis of Infinite-Dimensional Discrete Dynamical Systems,” SIAM Journal
on Applied Dynamical Systems, pp. 117–160, 2004.
mla: Day, S., et al. “A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional
Discrete Dynamical Systems.” SIAM Journal on Applied Dynamical Systems,
2004, pp. 117–60, doi:10.1137/030600210.
short: S. Day, O. Junge, K. Mischaikow, SIAM Journal on Applied Dynamical Systems
(2004) 117–160.
date_created: 2020-04-15T08:17:18Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1137/030600210
language:
- iso: eng
page: 117-160
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
issn:
- 1536-0040
publication_status: published
status: public
title: A Rigorous Numerical Method for the Global Analysis of Infinite-Dimensional
Discrete Dynamical Systems
type: journal_article
user_id: '15701'
year: '2004'
...
---
_id: '16619'
author:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Hinke M.
full_name: Osinga, Hinke M.
last_name: Osinga
citation:
ama: 'Junge O, Osinga HM. A set oriented approach to global optimal control. ESAIM:
Control, Optimisation and Calculus of Variations. 2004:259-270. doi:10.1051/cocv:2004006'
apa: 'Junge, O., & Osinga, H. M. (2004). A set oriented approach to global optimal
control. ESAIM: Control, Optimisation and Calculus of Variations, 259–270.
https://doi.org/10.1051/cocv:2004006'
bibtex: '@article{Junge_Osinga_2004, title={A set oriented approach to global optimal
control}, DOI={10.1051/cocv:2004006},
journal={ESAIM: Control, Optimisation and Calculus of Variations}, author={Junge,
Oliver and Osinga, Hinke M.}, year={2004}, pages={259–270} }'
chicago: 'Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global
Optimal Control.” ESAIM: Control, Optimisation and Calculus of Variations,
2004, 259–70. https://doi.org/10.1051/cocv:2004006.'
ieee: 'O. Junge and H. M. Osinga, “A set oriented approach to global optimal control,”
ESAIM: Control, Optimisation and Calculus of Variations, pp. 259–270, 2004.'
mla: 'Junge, Oliver, and Hinke M. Osinga. “A Set Oriented Approach to Global Optimal
Control.” ESAIM: Control, Optimisation and Calculus of Variations, 2004,
pp. 259–70, doi:10.1051/cocv:2004006.'
short: 'O. Junge, H.M. Osinga, ESAIM: Control, Optimisation and Calculus of Variations
(2004) 259–270.'
date_created: 2020-04-16T08:11:16Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1051/cocv:2004006
page: 259-270
publication: 'ESAIM: Control, Optimisation and Calculus of Variations'
publication_identifier:
issn:
- 1292-8119
- 1262-3377
publication_status: published
status: public
title: A set oriented approach to global optimal control
type: journal_article
user_id: '15701'
year: '2004'
...
---
_id: '16613'
author:
- first_name: Lars
full_name: Grüne, Lars
last_name: Grüne
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: Grüne L, Junge O. A set oriented approach to optimal feedback stabilization.
Systems & Control Letters. 2005:169-180. doi:10.1016/j.sysconle.2004.08.005
apa: Grüne, L., & Junge, O. (2005). A set oriented approach to optimal feedback
stabilization. Systems & Control Letters, 169–180. https://doi.org/10.1016/j.sysconle.2004.08.005
bibtex: '@article{Grüne_Junge_2005, title={A set oriented approach to optimal feedback
stabilization}, DOI={10.1016/j.sysconle.2004.08.005},
journal={Systems & Control Letters}, author={Grüne, Lars and Junge, Oliver},
year={2005}, pages={169–180} }'
chicago: Grüne, Lars, and Oliver Junge. “A Set Oriented Approach to Optimal Feedback
Stabilization.” Systems & Control Letters, 2005, 169–80. https://doi.org/10.1016/j.sysconle.2004.08.005.
ieee: L. Grüne and O. Junge, “A set oriented approach to optimal feedback stabilization,”
Systems & Control Letters, pp. 169–180, 2005.
mla: Grüne, Lars, and Oliver Junge. “A Set Oriented Approach to Optimal Feedback
Stabilization.” Systems & Control Letters, 2005, pp. 169–80, doi:10.1016/j.sysconle.2004.08.005.
short: L. Grüne, O. Junge, Systems & Control Letters (2005) 169–180.
date_created: 2020-04-16T08:04:26Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1016/j.sysconle.2004.08.005
language:
- iso: eng
page: 169-180
publication: Systems & Control Letters
publication_identifier:
issn:
- 0167-6911
publication_status: published
status: public
title: A set oriented approach to optimal feedback stabilization
type: journal_article
user_id: '15701'
year: '2005'
...
---
_id: '16581'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Adrian
full_name: Ziessler, Adrian
last_name: Ziessler
citation:
ama: Dellnitz M, Klus S, Ziessler A. A Set-Oriented Numerical Approach for Dynamical
Systems with Parameter Uncertainty. SIAM Journal on Applied Dynamical Systems.
2017:120-138. doi:10.1137/16m1072735
apa: Dellnitz, M., Klus, S., & Ziessler, A. (2017). A Set-Oriented Numerical
Approach for Dynamical Systems with Parameter Uncertainty. SIAM Journal on
Applied Dynamical Systems, 120–138. https://doi.org/10.1137/16m1072735
bibtex: '@article{Dellnitz_Klus_Ziessler_2017, title={A Set-Oriented Numerical Approach
for Dynamical Systems with Parameter Uncertainty}, DOI={10.1137/16m1072735},
journal={SIAM Journal on Applied Dynamical Systems}, author={Dellnitz, Michael
and Klus, Stefan and Ziessler, Adrian}, year={2017}, pages={120–138} }'
chicago: Dellnitz, Michael, Stefan Klus, and Adrian Ziessler. “A Set-Oriented Numerical
Approach for Dynamical Systems with Parameter Uncertainty.” SIAM Journal on
Applied Dynamical Systems, 2017, 120–38. https://doi.org/10.1137/16m1072735.
ieee: M. Dellnitz, S. Klus, and A. Ziessler, “A Set-Oriented Numerical Approach
for Dynamical Systems with Parameter Uncertainty,” SIAM Journal on Applied
Dynamical Systems, pp. 120–138, 2017.
mla: Dellnitz, Michael, et al. “A Set-Oriented Numerical Approach for Dynamical
Systems with Parameter Uncertainty.” SIAM Journal on Applied Dynamical Systems,
2017, pp. 120–38, doi:10.1137/16m1072735.
short: M. Dellnitz, S. Klus, A. Ziessler, SIAM Journal on Applied Dynamical Systems
(2017) 120–138.
date_created: 2020-04-16T05:39:17Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1137/16m1072735
language:
- iso: eng
page: 120-138
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
issn:
- 1536-0040
publication_status: published
status: public
title: A Set-Oriented Numerical Approach for Dynamical Systems with Parameter Uncertainty
type: journal_article
user_id: '15701'
year: '2017'
...
---
_id: '16710'
abstract:
- lang: eng
text: "In this work we present a set-oriented path following method for the computation
of relative global\r\nattractors of parameter-dependent dynamical systems. We
start with an initial approximation of the\r\nrelative global attractor for a
fixed parameter λ0 computed by a set-oriented subdivision method.\r\nBy using
previously obtained approximations of the parameter-dependent relative global
attractor\r\nwe can track it with respect to a one-dimensional parameter λ > λ0
without restarting the whole\r\nsubdivision procedure. We illustrate the feasibility
of the set-oriented path following method by\r\nexploring the dynamics in low-dimensional
models for shear flows during the transition to turbulence\r\nand of large-scale
atmospheric regime changes .\r\n"
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
- first_name: Adrian
full_name: Ziessler, Adrian
last_name: Ziessler
- first_name: Bruno
full_name: Eckhardt, Bruno
last_name: Eckhardt
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Gerlach R, Ziessler A, Eckhardt B, Dellnitz M. A Set-Oriented Path Following
Method for the Approximation of Parameter Dependent Attractors. SIAM Journal
on Applied Dynamical Systems. Published online 2020:705-723. doi:10.1137/19m1247139
apa: Gerlach, R., Ziessler, A., Eckhardt, B., & Dellnitz, M. (2020). A Set-Oriented
Path Following Method for the Approximation of Parameter Dependent Attractors.
SIAM Journal on Applied Dynamical Systems, 705–723. https://doi.org/10.1137/19m1247139
bibtex: '@article{Gerlach_Ziessler_Eckhardt_Dellnitz_2020, title={A Set-Oriented
Path Following Method for the Approximation of Parameter Dependent Attractors},
DOI={10.1137/19m1247139}, journal={SIAM
Journal on Applied Dynamical Systems}, author={Gerlach, Raphael and Ziessler,
Adrian and Eckhardt, Bruno and Dellnitz, Michael}, year={2020}, pages={705–723}
}'
chicago: Gerlach, Raphael, Adrian Ziessler, Bruno Eckhardt, and Michael Dellnitz.
“A Set-Oriented Path Following Method for the Approximation of Parameter Dependent
Attractors.” SIAM Journal on Applied Dynamical Systems, 2020, 705–23. https://doi.org/10.1137/19m1247139.
ieee: 'R. Gerlach, A. Ziessler, B. Eckhardt, and M. Dellnitz, “A Set-Oriented Path
Following Method for the Approximation of Parameter Dependent Attractors,” SIAM
Journal on Applied Dynamical Systems, pp. 705–723, 2020, doi: 10.1137/19m1247139.'
mla: Gerlach, Raphael, et al. “A Set-Oriented Path Following Method for the Approximation
of Parameter Dependent Attractors.” SIAM Journal on Applied Dynamical Systems,
2020, pp. 705–23, doi:10.1137/19m1247139.
short: R. Gerlach, A. Ziessler, B. Eckhardt, M. Dellnitz, SIAM Journal on Applied
Dynamical Systems (2020) 705–723.
date_created: 2020-04-16T14:05:41Z
date_updated: 2022-06-21T09:18:46Z
department:
- _id: '101'
doi: 10.1137/19m1247139
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://epubs.siam.org/doi/epdf/10.1137/19M1247139
oa: '1'
page: 705-723
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
issn:
- 1536-0040
publication_status: published
status: public
title: A Set-Oriented Path Following Method for the Approximation of Parameter Dependent
Attractors
type: journal_article
user_id: '32655'
year: '2020'
...
---
_id: '17015'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Andreas
full_name: Hohmann, Andreas
last_name: Hohmann
citation:
ama: Dellnitz M, Hohmann A. A subdivision algorithm for the computation of unstable
manifolds and global attractors. Numerische Mathematik. 1997;75:293-317.
doi:10.1007/s002110050240
apa: Dellnitz, M., & Hohmann, A. (1997). A subdivision algorithm for the computation
of unstable manifolds and global attractors. Numerische Mathematik, 75,
293–317. https://doi.org/10.1007/s002110050240
bibtex: '@article{Dellnitz_Hohmann_1997, title={A subdivision algorithm for the
computation of unstable manifolds and global attractors}, volume={75}, DOI={10.1007/s002110050240}, journal={Numerische
Mathematik}, author={Dellnitz, Michael and Hohmann, Andreas}, year={1997}, pages={293–317}
}'
chicago: 'Dellnitz, Michael, and Andreas Hohmann. “A Subdivision Algorithm for the
Computation of Unstable Manifolds and Global Attractors.” Numerische Mathematik
75 (1997): 293–317. https://doi.org/10.1007/s002110050240.'
ieee: M. Dellnitz and A. Hohmann, “A subdivision algorithm for the computation of
unstable manifolds and global attractors,” Numerische Mathematik, vol.
75, pp. 293–317, 1997.
mla: Dellnitz, Michael, and Andreas Hohmann. “A Subdivision Algorithm for the Computation
of Unstable Manifolds and Global Attractors.” Numerische Mathematik, vol.
75, 1997, pp. 293–317, doi:10.1007/s002110050240.
short: M. Dellnitz, A. Hohmann, Numerische Mathematik 75 (1997) 293–317.
date_created: 2020-05-19T09:07:27Z
date_updated: 2022-01-06T06:53:02Z
department:
- _id: '101'
doi: 10.1007/s002110050240
intvolume: ' 75'
language:
- iso: eng
page: 293-317
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
status: public
title: A subdivision algorithm for the computation of unstable manifolds and global
attractors
type: journal_article
user_id: '32643'
volume: 75
year: '1997'
...
---
_id: '16627'
abstract:
- lang: eng
text: The computation of global invariant manifolds has seen renewed interest
in recent years. We survey different approaches for computing a global stable
or unstable manifold of a vector field, where we concentrate on the case of a
two-dimensional manifold. All methods are illustrated with the same example —
the two-dimensional stable manifold of the origin in the Lorenz system.
author:
- first_name: B.
full_name: Krauskopf, B.
last_name: Krauskopf
- first_name: H. M.
full_name: Osinga, H. M.
last_name: Osinga
- first_name: E. J.
full_name: Doedel, E. J.
last_name: Doedel
- first_name: M. E.
full_name: Henderson, M. E.
last_name: Henderson
- first_name: J.
full_name: Guckenheimer, J.
last_name: Guckenheimer
- first_name: A.
full_name: Vladimirsky, A.
last_name: Vladimirsky
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
- first_name: O.
full_name: Junge, O.
last_name: Junge
citation:
ama: Krauskopf B, Osinga HM, Doedel EJ, et al. A Survey of Methods for Computing
(un)stable Manifolds of Vector Fields. International Journal of Bifurcation
and Chaos. 2005:763-791. doi:10.1142/s0218127405012533
apa: Krauskopf, B., Osinga, H. M., Doedel, E. J., Henderson, M. E., Guckenheimer,
J., Vladimirsky, A., … Junge, O. (2005). A Survey of Methods for Computing (un)stable
Manifolds of Vector Fields. International Journal of Bifurcation and Chaos,
763–791. https://doi.org/10.1142/s0218127405012533
bibtex: '@article{Krauskopf_Osinga_Doedel_Henderson_Guckenheimer_Vladimirsky_Dellnitz_Junge_2005,
title={A Survey of Methods for Computing (un)stable Manifolds of Vector Fields},
DOI={10.1142/s0218127405012533},
journal={International Journal of Bifurcation and Chaos}, author={Krauskopf, B.
and Osinga, H. M. and Doedel, E. J. and Henderson, M. E. and Guckenheimer, J.
and Vladimirsky, A. and Dellnitz, M. and Junge, O.}, year={2005}, pages={763–791}
}'
chicago: Krauskopf, B., H. M. Osinga, E. J. Doedel, M. E. Henderson, J. Guckenheimer,
A. Vladimirsky, M. Dellnitz, and O. Junge. “A Survey of Methods for Computing
(Un)Stable Manifolds of Vector Fields.” International Journal of Bifurcation
and Chaos, 2005, 763–91. https://doi.org/10.1142/s0218127405012533.
ieee: B. Krauskopf et al., “A Survey of Methods for Computing (un)stable
Manifolds of Vector Fields,” International Journal of Bifurcation and Chaos,
pp. 763–791, 2005.
mla: Krauskopf, B., et al. “A Survey of Methods for Computing (Un)Stable Manifolds
of Vector Fields.” International Journal of Bifurcation and Chaos, 2005,
pp. 763–91, doi:10.1142/s0218127405012533.
short: B. Krauskopf, H.M. Osinga, E.J. Doedel, M.E. Henderson, J. Guckenheimer,
A. Vladimirsky, M. Dellnitz, O. Junge, International Journal of Bifurcation and
Chaos (2005) 763–791.
date_created: 2020-04-16T08:21:52Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1142/s0218127405012533
language:
- iso: eng
page: 763-791
publication: International Journal of Bifurcation and Chaos
publication_identifier:
issn:
- 0218-1274
- 1793-6551
publication_status: published
status: public
title: A Survey of Methods for Computing (un)stable Manifolds of Vector Fields
type: journal_article
user_id: '15701'
year: '2005'
...
---
_id: '8751'
abstract:
- lang: eng
text: Multiobjective optimization plays an increasingly important role in modern
applications, where several criteria are often of equal importance. The task in
multiobjective optimization and multiobjective optimal control is therefore to
compute the set of optimal compromises (the Pareto set) between the conflicting
objectives. The advances in algorithms and the increasing interest in Pareto-optimal
solutions have led to a wide range of new applications related to optimal and
feedback control, which results in new challenges such as expensive models or
real-time applicability. Since the Pareto set generally consists of an infinite
number of solutions, the computational effort can quickly become challenging,
which is particularly problematic when the objectives are costly to evaluate or
when a solution has to be presented very quickly. This article gives an overview
of recent developments in accelerating multiobjective optimal control for complex
problems where either PDE constraints are present or where a feedback behavior
has to be achieved. In the first case, surrogate models yield significant speed-ups.
Besides classical meta-modeling techniques for multiobjective optimization, a
promising alternative for control problems is to introduce a surrogate model for
the system dynamics. In the case of real-time requirements, various promising
model predictive control approaches have been proposed, using either fast online
solvers or offline-online decomposition. We also briefly comment on dimension
reduction in many-objective optimization problems as another technique for reducing
the numerical effort.
article_type: review
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Peitz S, Dellnitz M. A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate
Models, Feedback Control and Objective Reduction. Mathematical and Computational
Applications. 2018;23(2). doi:10.3390/mca23020030
apa: Peitz, S., & Dellnitz, M. (2018). A Survey of Recent Trends in Multiobjective
Optimal Control—Surrogate Models, Feedback Control and Objective Reduction. Mathematical
and Computational Applications, 23(2). https://doi.org/10.3390/mca23020030
bibtex: '@article{Peitz_Dellnitz_2018, title={A Survey of Recent Trends in Multiobjective
Optimal Control—Surrogate Models, Feedback Control and Objective Reduction}, volume={23},
DOI={10.3390/mca23020030}, number={2},
journal={Mathematical and Computational Applications}, author={Peitz, Sebastian
and Dellnitz, Michael}, year={2018} }'
chicago: Peitz, Sebastian, and Michael Dellnitz. “A Survey of Recent Trends in Multiobjective
Optimal Control—Surrogate Models, Feedback Control and Objective Reduction.” Mathematical
and Computational Applications 23, no. 2 (2018). https://doi.org/10.3390/mca23020030.
ieee: S. Peitz and M. Dellnitz, “A Survey of Recent Trends in Multiobjective Optimal
Control—Surrogate Models, Feedback Control and Objective Reduction,” Mathematical
and Computational Applications, vol. 23, no. 2, 2018.
mla: Peitz, Sebastian, and Michael Dellnitz. “A Survey of Recent Trends in Multiobjective
Optimal Control—Surrogate Models, Feedback Control and Objective Reduction.” Mathematical
and Computational Applications, vol. 23, no. 2, 2018, doi:10.3390/mca23020030.
short: S. Peitz, M. Dellnitz, Mathematical and Computational Applications 23 (2018).
date_created: 2019-03-29T13:27:51Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.3390/mca23020030
intvolume: ' 23'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/2297-8747/23/2/30/pdf
oa: '1'
publication: Mathematical and Computational Applications
publication_identifier:
issn:
- 2297-8747
publication_status: published
status: public
title: A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models,
Feedback Control and Objective Reduction
type: journal_article
user_id: '47427'
volume: 23
year: '2018'
...
---
_id: '16677'
author:
- first_name: Katrin
full_name: Witting, Katrin
last_name: Witting
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Witting K, Ober-Blöbaum S, Dellnitz M. A variational approach to define robustness
for parametric multiobjective optimization problems. Journal of Global Optimization.
2013:331-345. doi:10.1007/s10898-012-9972-6
apa: Witting, K., Ober-Blöbaum, S., & Dellnitz, M. (2013). A variational approach
to define robustness for parametric multiobjective optimization problems. Journal
of Global Optimization, 331–345. https://doi.org/10.1007/s10898-012-9972-6
bibtex: '@article{Witting_Ober-Blöbaum_Dellnitz_2013, title={A variational approach
to define robustness for parametric multiobjective optimization problems}, DOI={10.1007/s10898-012-9972-6},
journal={Journal of Global Optimization}, author={Witting, Katrin and Ober-Blöbaum,
Sina and Dellnitz, Michael}, year={2013}, pages={331–345} }'
chicago: Witting, Katrin, Sina Ober-Blöbaum, and Michael Dellnitz. “A Variational
Approach to Define Robustness for Parametric Multiobjective Optimization Problems.”
Journal of Global Optimization, 2013, 331–45. https://doi.org/10.1007/s10898-012-9972-6.
ieee: K. Witting, S. Ober-Blöbaum, and M. Dellnitz, “A variational approach to define
robustness for parametric multiobjective optimization problems,” Journal of
Global Optimization, pp. 331–345, 2013.
mla: Witting, Katrin, et al. “A Variational Approach to Define Robustness for Parametric
Multiobjective Optimization Problems.” Journal of Global Optimization,
2013, pp. 331–45, doi:10.1007/s10898-012-9972-6.
short: K. Witting, S. Ober-Blöbaum, M. Dellnitz, Journal of Global Optimization
(2013) 331–345.
date_created: 2020-04-16T10:14:04Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/s10898-012-9972-6
language:
- iso: eng
page: 331-345
publication: Journal of Global Optimization
publication_identifier:
issn:
- 0925-5001
- 1573-2916
publication_status: published
status: public
title: A variational approach to define robustness for parametric multiobjective optimization
problems
type: journal_article
user_id: '15701'
year: '2013'
...
---
_id: '21935'
author:
- first_name: Frank
full_name: Noé, Frank
last_name: Noé
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
citation:
ama: Noé F, Nüske F. A Variational Approach to Modeling Slow Processes in Stochastic
Dynamical Systems. Multiscale Modeling & Simulation. 2013:635-655.
doi:10.1137/110858616
apa: Noé, F., & Nüske, F. (2013). A Variational Approach to Modeling Slow Processes
in Stochastic Dynamical Systems. Multiscale Modeling & Simulation,
635–655. https://doi.org/10.1137/110858616
bibtex: '@article{Noé_Nüske_2013, title={A Variational Approach to Modeling Slow
Processes in Stochastic Dynamical Systems}, DOI={10.1137/110858616},
journal={Multiscale Modeling & Simulation}, author={Noé, Frank and Nüske,
Feliks}, year={2013}, pages={635–655} }'
chicago: Noé, Frank, and Feliks Nüske. “A Variational Approach to Modeling Slow
Processes in Stochastic Dynamical Systems.” Multiscale Modeling & Simulation,
2013, 635–55. https://doi.org/10.1137/110858616.
ieee: F. Noé and F. Nüske, “A Variational Approach to Modeling Slow Processes in
Stochastic Dynamical Systems,” Multiscale Modeling & Simulation, pp.
635–655, 2013.
mla: Noé, Frank, and Feliks Nüske. “A Variational Approach to Modeling Slow Processes
in Stochastic Dynamical Systems.” Multiscale Modeling & Simulation,
2013, pp. 635–55, doi:10.1137/110858616.
short: F. Noé, F. Nüske, Multiscale Modeling & Simulation (2013) 635–655.
date_created: 2021-04-30T16:51:37Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1137/110858616
extern: '1'
language:
- iso: eng
page: 635-655
publication: Multiscale Modeling & Simulation
publication_identifier:
issn:
- 1540-3459
- 1540-3467
publication_status: published
status: public
title: A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems
type: journal_article
user_id: '81513'
year: '2013'
...
---
_id: '16532'
author:
- first_name: M
full_name: Dellnitz, M
last_name: Dellnitz
- first_name: C
full_name: Heinrich, C
last_name: Heinrich
citation:
ama: Dellnitz M, Heinrich C. Admissible symmetry increasing bifurcations. Nonlinearity.
1995:1039-1066. doi:10.1088/0951-7715/8/6/009
apa: Dellnitz, M., & Heinrich, C. (1995). Admissible symmetry increasing bifurcations.
Nonlinearity, 1039–1066. https://doi.org/10.1088/0951-7715/8/6/009
bibtex: '@article{Dellnitz_Heinrich_1995, title={Admissible symmetry increasing
bifurcations}, DOI={10.1088/0951-7715/8/6/009},
journal={Nonlinearity}, author={Dellnitz, M and Heinrich, C}, year={1995}, pages={1039–1066}
}'
chicago: Dellnitz, M, and C Heinrich. “Admissible Symmetry Increasing Bifurcations.”
Nonlinearity, 1995, 1039–66. https://doi.org/10.1088/0951-7715/8/6/009.
ieee: M. Dellnitz and C. Heinrich, “Admissible symmetry increasing bifurcations,”
Nonlinearity, pp. 1039–1066, 1995.
mla: Dellnitz, M., and C. Heinrich. “Admissible Symmetry Increasing Bifurcations.”
Nonlinearity, 1995, pp. 1039–66, doi:10.1088/0951-7715/8/6/009.
short: M. Dellnitz, C. Heinrich, Nonlinearity (1995) 1039–1066.
date_created: 2020-04-15T08:25:12Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1088/0951-7715/8/6/009
language:
- iso: eng
page: 1039-1066
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Admissible symmetry increasing bifurcations
type: journal_article
user_id: '15701'
year: '1995'
...
---
_id: '16714'
author:
- first_name: Solveig
full_name: Vieluf, Solveig
last_name: Vieluf
- first_name: Karin
full_name: Mora, Karin
last_name: Mora
- first_name: Christian
full_name: Gölz, Christian
last_name: Gölz
- first_name: Eva-Maria
full_name: Reuter, Eva-Maria
last_name: Reuter
- first_name: Ben
full_name: Godde, Ben
last_name: Godde
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Claus
full_name: Reinsberger, Claus
last_name: Reinsberger
- first_name: Claudia
full_name: Voelcker-Rehage, Claudia
last_name: Voelcker-Rehage
citation:
ama: Vieluf S, Mora K, Gölz C, et al. Age- and Expertise-Related Differences of
Sensorimotor Network Dynamics during Force Control. Neuroscience. 2018:203-213.
doi:10.1016/j.neuroscience.2018.07.025
apa: Vieluf, S., Mora, K., Gölz, C., Reuter, E.-M., Godde, B., Dellnitz, M., … Voelcker-Rehage,
C. (2018). Age- and Expertise-Related Differences of Sensorimotor Network Dynamics
during Force Control. Neuroscience, 203–213. https://doi.org/10.1016/j.neuroscience.2018.07.025
bibtex: '@article{Vieluf_Mora_Gölz_Reuter_Godde_Dellnitz_Reinsberger_Voelcker-Rehage_2018,
title={Age- and Expertise-Related Differences of Sensorimotor Network Dynamics
during Force Control}, DOI={10.1016/j.neuroscience.2018.07.025},
journal={Neuroscience}, author={Vieluf, Solveig and Mora, Karin and Gölz, Christian
and Reuter, Eva-Maria and Godde, Ben and Dellnitz, Michael and Reinsberger, Claus
and Voelcker-Rehage, Claudia}, year={2018}, pages={203–213} }'
chicago: Vieluf, Solveig, Karin Mora, Christian Gölz, Eva-Maria Reuter, Ben Godde,
Michael Dellnitz, Claus Reinsberger, and Claudia Voelcker-Rehage. “Age- and Expertise-Related
Differences of Sensorimotor Network Dynamics during Force Control.” Neuroscience,
2018, 203–13. https://doi.org/10.1016/j.neuroscience.2018.07.025.
ieee: S. Vieluf et al., “Age- and Expertise-Related Differences of Sensorimotor
Network Dynamics during Force Control,” Neuroscience, pp. 203–213, 2018.
mla: Vieluf, Solveig, et al. “Age- and Expertise-Related Differences of Sensorimotor
Network Dynamics during Force Control.” Neuroscience, 2018, pp. 203–13,
doi:10.1016/j.neuroscience.2018.07.025.
short: S. Vieluf, K. Mora, C. Gölz, E.-M. Reuter, B. Godde, M. Dellnitz, C. Reinsberger,
C. Voelcker-Rehage, Neuroscience (2018) 203–213.
date_created: 2020-04-16T14:08:51Z
date_updated: 2022-01-06T06:52:55Z
department:
- _id: '101'
doi: 10.1016/j.neuroscience.2018.07.025
language:
- iso: eng
page: 203-213
publication: Neuroscience
publication_identifier:
issn:
- 0306-4522
publication_status: published
status: public
title: Age- and Expertise-Related Differences of Sensorimotor Network Dynamics during
Force Control
type: journal_article
user_id: '47427'
year: '2018'
...
---
_id: '16535'
abstract:
- lang: eng
text: Recently multilevel subdivision techniques have been introduced in
the numerical investigation of complicated dynamical behavior. We illustrate the
applicability and efficiency of these methods by a detailed numerical study of
Chua's circuit. In particular we will show that there exist two regions in phase
space which are almost invariant in the sense that typical trajectories stay inside
each of these sets on average for quite a long time.
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: Dellnitz M, Junge O. Almost Invariant Sets in Chua’s Circuit. International
Journal of Bifurcation and Chaos. 1997:2475-2485. doi:10.1142/s0218127497001655
apa: Dellnitz, M., & Junge, O. (1997). Almost Invariant Sets in Chua’s Circuit.
International Journal of Bifurcation and Chaos, 2475–2485. https://doi.org/10.1142/s0218127497001655
bibtex: '@article{Dellnitz_Junge_1997, title={Almost Invariant Sets in Chua’s Circuit},
DOI={10.1142/s0218127497001655},
journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael
and Junge, Oliver}, year={1997}, pages={2475–2485} }'
chicago: Dellnitz, Michael, and Oliver Junge. “Almost Invariant Sets in Chua’s Circuit.”
International Journal of Bifurcation and Chaos, 1997, 2475–85. https://doi.org/10.1142/s0218127497001655.
ieee: M. Dellnitz and O. Junge, “Almost Invariant Sets in Chua’s Circuit,” International
Journal of Bifurcation and Chaos, pp. 2475–2485, 1997.
mla: Dellnitz, Michael, and Oliver Junge. “Almost Invariant Sets in Chua’s Circuit.”
International Journal of Bifurcation and Chaos, 1997, pp. 2475–85, doi:10.1142/s0218127497001655.
short: M. Dellnitz, O. Junge, International Journal of Bifurcation and Chaos (1997)
2475–2485.
date_created: 2020-04-15T08:31:50Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1142/s0218127497001655
language:
- iso: eng
page: 2475-2485
publication: International Journal of Bifurcation and Chaos
publication_identifier:
issn:
- 0218-1274
- 1793-6551
publication_status: published
status: public
title: Almost Invariant Sets in Chua's Circuit
type: journal_article
user_id: '15701'
year: '1997'
...
---
_id: '16614'
author:
- first_name: Rabbijah
full_name: Guder, Rabbijah
last_name: Guder
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Edwin
full_name: Kreuzer, Edwin
last_name: Kreuzer
citation:
ama: Guder R, Dellnitz M, Kreuzer E. An adaptive method for the approximation of
the generalized cell mapping. Chaos, Solitons & Fractals. 1997:525-534.
doi:10.1016/s0960-0779(96)00118-x
apa: Guder, R., Dellnitz, M., & Kreuzer, E. (1997). An adaptive method for the
approximation of the generalized cell mapping. Chaos, Solitons & Fractals,
525–534. https://doi.org/10.1016/s0960-0779(96)00118-x
bibtex: '@article{Guder_Dellnitz_Kreuzer_1997, title={An adaptive method for the
approximation of the generalized cell mapping}, DOI={10.1016/s0960-0779(96)00118-x},
journal={Chaos, Solitons & Fractals}, author={Guder, Rabbijah and Dellnitz,
Michael and Kreuzer, Edwin}, year={1997}, pages={525–534} }'
chicago: Guder, Rabbijah, Michael Dellnitz, and Edwin Kreuzer. “An Adaptive Method
for the Approximation of the Generalized Cell Mapping.” Chaos, Solitons &
Fractals, 1997, 525–34. https://doi.org/10.1016/s0960-0779(96)00118-x.
ieee: R. Guder, M. Dellnitz, and E. Kreuzer, “An adaptive method for the approximation
of the generalized cell mapping,” Chaos, Solitons & Fractals, pp. 525–534,
1997.
mla: Guder, Rabbijah, et al. “An Adaptive Method for the Approximation of the Generalized
Cell Mapping.” Chaos, Solitons & Fractals, 1997, pp. 525–34, doi:10.1016/s0960-0779(96)00118-x.
short: R. Guder, M. Dellnitz, E. Kreuzer, Chaos, Solitons & Fractals (1997)
525–534.
date_created: 2020-04-16T08:05:37Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1016/s0960-0779(96)00118-x
language:
- iso: eng
page: 525-534
publication: Chaos, Solitons & Fractals
publication_identifier:
issn:
- 0960-0779
publication_status: published
status: public
title: An adaptive method for the approximation of the generalized cell mapping
type: journal_article
user_id: '15701'
year: '1997'
...
---
_id: '16536'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: Dellnitz M, Junge O. An adaptive subdivision technique for the approximation
of attractors and invariant measures. Computing and Visualization in Science.
1998:63-68. doi:10.1007/s007910050006
apa: Dellnitz, M., & Junge, O. (1998). An adaptive subdivision technique for
the approximation of attractors and invariant measures. Computing and Visualization
in Science, 63–68. https://doi.org/10.1007/s007910050006
bibtex: '@article{Dellnitz_Junge_1998, title={An adaptive subdivision technique
for the approximation of attractors and invariant measures}, DOI={10.1007/s007910050006},
journal={Computing and Visualization in Science}, author={Dellnitz, Michael and
Junge, Oliver}, year={1998}, pages={63–68} }'
chicago: Dellnitz, Michael, and Oliver Junge. “An Adaptive Subdivision Technique
for the Approximation of Attractors and Invariant Measures.” Computing and
Visualization in Science, 1998, 63–68. https://doi.org/10.1007/s007910050006.
ieee: M. Dellnitz and O. Junge, “An adaptive subdivision technique for the approximation
of attractors and invariant measures,” Computing and Visualization in Science,
pp. 63–68, 1998.
mla: Dellnitz, Michael, and Oliver Junge. “An Adaptive Subdivision Technique for
the Approximation of Attractors and Invariant Measures.” Computing and Visualization
in Science, 1998, pp. 63–68, doi:10.1007/s007910050006.
short: M. Dellnitz, O. Junge, Computing and Visualization in Science (1998) 63–68.
date_created: 2020-04-15T08:33:03Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/s007910050006
language:
- iso: eng
page: 63-68
publication: Computing and Visualization in Science
publication_identifier:
issn:
- 1432-9360
- 1433-0369
publication_status: published
status: public
title: An adaptive subdivision technique for the approximation of attractors and invariant
measures
type: journal_article
user_id: '15701'
year: '1998'
...
---
_id: '16617'
author:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: 'Junge O. An adaptive subdivision technique for the approximation of attractors
and invariant measures: proof of convergence. Dynamical Systems. 2001:213-222.
doi:10.1080/14689360109696233'
apa: 'Junge, O. (2001). An adaptive subdivision technique for the approximation
of attractors and invariant measures: proof of convergence. Dynamical Systems,
213–222. https://doi.org/10.1080/14689360109696233'
bibtex: '@article{Junge_2001, title={An adaptive subdivision technique for the approximation
of attractors and invariant measures: proof of convergence}, DOI={10.1080/14689360109696233},
journal={Dynamical Systems}, author={Junge, Oliver}, year={2001}, pages={213–222}
}'
chicago: 'Junge, Oliver. “An Adaptive Subdivision Technique for the Approximation
of Attractors and Invariant Measures: Proof of Convergence.” Dynamical Systems,
2001, 213–22. https://doi.org/10.1080/14689360109696233.'
ieee: 'O. Junge, “An adaptive subdivision technique for the approximation of attractors
and invariant measures: proof of convergence,” Dynamical Systems, pp. 213–222,
2001.'
mla: 'Junge, Oliver. “An Adaptive Subdivision Technique for the Approximation of
Attractors and Invariant Measures: Proof of Convergence.” Dynamical Systems,
2001, pp. 213–22, doi:10.1080/14689360109696233.'
short: O. Junge, Dynamical Systems (2001) 213–222.
date_created: 2020-04-16T08:09:10Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1080/14689360109696233
language:
- iso: eng
page: 213-222
publication: Dynamical Systems
publication_identifier:
issn:
- 1468-9367
- 1468-9375
publication_status: published
status: public
title: 'An adaptive subdivision technique for the approximation of attractors and
invariant measures: proof of convergence'
type: journal_article
user_id: '15701'
year: '2001'
...
---
_id: '16624'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Tuhin
full_name: Sahai, Tuhin
last_name: Sahai
- first_name: Cong
full_name: Liu, Cong
last_name: Liu
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Klus S, Sahai T, Liu C, Dellnitz M. An efficient algorithm for the parallel
solution of high-dimensional differential equations. Journal of Computational
and Applied Mathematics. 2011:3053-3062. doi:10.1016/j.cam.2010.12.026
apa: Klus, S., Sahai, T., Liu, C., & Dellnitz, M. (2011). An efficient algorithm
for the parallel solution of high-dimensional differential equations. Journal
of Computational and Applied Mathematics, 3053–3062. https://doi.org/10.1016/j.cam.2010.12.026
bibtex: '@article{Klus_Sahai_Liu_Dellnitz_2011, title={An efficient algorithm for
the parallel solution of high-dimensional differential equations}, DOI={10.1016/j.cam.2010.12.026},
journal={Journal of Computational and Applied Mathematics}, author={Klus, Stefan
and Sahai, Tuhin and Liu, Cong and Dellnitz, Michael}, year={2011}, pages={3053–3062}
}'
chicago: Klus, Stefan, Tuhin Sahai, Cong Liu, and Michael Dellnitz. “An Efficient
Algorithm for the Parallel Solution of High-Dimensional Differential Equations.”
Journal of Computational and Applied Mathematics, 2011, 3053–62. https://doi.org/10.1016/j.cam.2010.12.026.
ieee: S. Klus, T. Sahai, C. Liu, and M. Dellnitz, “An efficient algorithm for the
parallel solution of high-dimensional differential equations,” Journal of Computational
and Applied Mathematics, pp. 3053–3062, 2011.
mla: Klus, Stefan, et al. “An Efficient Algorithm for the Parallel Solution of High-Dimensional
Differential Equations.” Journal of Computational and Applied Mathematics,
2011, pp. 3053–62, doi:10.1016/j.cam.2010.12.026.
short: S. Klus, T. Sahai, C. Liu, M. Dellnitz, Journal of Computational and Applied
Mathematics (2011) 3053–3062.
date_created: 2020-04-16T08:18:33Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1016/j.cam.2010.12.026
language:
- iso: eng
page: 3053-3062
publication: Journal of Computational and Applied Mathematics
publication_identifier:
issn:
- 0377-0427
publication_status: published
status: public
title: An efficient algorithm for the parallel solution of high-dimensional differential
equations
type: journal_article
user_id: '15701'
year: '2011'
...
---
_id: '16867'
abstract:
- lang: eng
text: "In this article, we present an efficient descent method for locally Lipschitz\r\ncontinuous
multiobjective optimization problems (MOPs). The method is realized\r\nby combining
a theoretical result regarding the computation of descent\r\ndirections for nonsmooth
MOPs with a practical method to approximate the\r\nsubdifferentials of the objective
functions. We show convergence to points\r\nwhich satisfy a necessary condition
for Pareto optimality. Using a set of test\r\nproblems, we compare our method
to the multiobjective proximal bundle method by\r\nM\\\"akel\\\"a. The results
indicate that our method is competitive while being\r\neasier to implement. While
the number of objective function evaluations is\r\nlarger, the overall number
of subgradient evaluations is lower. Finally, we\r\nshow that our method can be
combined with a subdivision algorithm to compute\r\nentire Pareto sets of nonsmooth
MOPs."
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Gebken B, Peitz S. An efficient descent method for locally Lipschitz multiobjective
optimization problems. Journal of Optimization Theory and Applications.
2021;188:696-723. doi:10.1007/s10957-020-01803-w
apa: Gebken, B., & Peitz, S. (2021). An efficient descent method for locally
Lipschitz multiobjective optimization problems. Journal of Optimization Theory
and Applications, 188, 696–723. https://doi.org/10.1007/s10957-020-01803-w
bibtex: '@article{Gebken_Peitz_2021, title={An efficient descent method for locally
Lipschitz multiobjective optimization problems}, volume={188}, DOI={10.1007/s10957-020-01803-w},
journal={Journal of Optimization Theory and Applications}, author={Gebken, Bennet
and Peitz, Sebastian}, year={2021}, pages={696–723} }'
chicago: 'Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for
Locally Lipschitz Multiobjective Optimization Problems.” Journal of Optimization
Theory and Applications 188 (2021): 696–723. https://doi.org/10.1007/s10957-020-01803-w.'
ieee: B. Gebken and S. Peitz, “An efficient descent method for locally Lipschitz
multiobjective optimization problems,” Journal of Optimization Theory and Applications,
vol. 188, pp. 696–723, 2021.
mla: Gebken, Bennet, and Sebastian Peitz. “An Efficient Descent Method for Locally
Lipschitz Multiobjective Optimization Problems.” Journal of Optimization Theory
and Applications, vol. 188, 2021, pp. 696–723, doi:10.1007/s10957-020-01803-w.
short: B. Gebken, S. Peitz, Journal of Optimization Theory and Applications 188
(2021) 696–723.
date_created: 2020-04-27T09:11:22Z
date_updated: 2022-01-06T06:52:57Z
department:
- _id: '101'
doi: 10.1007/s10957-020-01803-w
intvolume: ' 188'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10957-020-01803-w.pdf
oa: '1'
page: 696-723
publication: Journal of Optimization Theory and Applications
publication_status: published
status: public
title: An efficient descent method for locally Lipschitz multiobjective optimization
problems
type: journal_article
user_id: '47427'
volume: 188
year: '2021'
...
---
_id: '17048'
author:
- first_name: Robert
full_name: Timmermann, Robert
last_name: Timmermann
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Timmermann R, Dellnitz M. Analysis of team and player performance using recorded
trajectory data. In: Performance Analysis of Sport IX, Part 8, Routledge.
; 2013.'
apa: Timmermann, R., & Dellnitz, M. (2013). Analysis of team and player performance
using recorded trajectory data. In Performance Analysis of Sport IX, Part 8,
Routledge.
bibtex: '@inproceedings{Timmermann_Dellnitz_2013, title={Analysis of team and player
performance using recorded trajectory data}, booktitle={Performance Analysis of
Sport IX, Part 8, Routledge}, author={Timmermann, Robert and Dellnitz, Michael},
year={2013} }'
chicago: Timmermann, Robert, and Michael Dellnitz. “Analysis of Team and Player
Performance Using Recorded Trajectory Data.” In Performance Analysis of Sport
IX, Part 8, Routledge, 2013.
ieee: R. Timmermann and M. Dellnitz, “Analysis of team and player performance using
recorded trajectory data,” in Performance Analysis of Sport IX, Part 8, Routledge,
2013.
mla: Timmermann, Robert, and Michael Dellnitz. “Analysis of Team and Player Performance
Using Recorded Trajectory Data.” Performance Analysis of Sport IX, Part 8,
Routledge, 2013.
short: 'R. Timmermann, M. Dellnitz, in: Performance Analysis of Sport IX, Part 8,
Routledge, 2013.'
date_created: 2020-05-20T08:42:19Z
date_updated: 2022-01-06T06:53:03Z
department:
- _id: '101'
language:
- iso: eng
publication: Performance Analysis of Sport IX, Part 8, Routledge
status: public
title: Analysis of team and player performance using recorded trajectory data
type: conference
user_id: '47427'
year: '2013'
...
---
_id: '16293'
abstract:
- lang: eng
text: "Kernel transfer operators, which can be regarded as approximations of\r\ntransfer
operators such as the Perron-Frobenius or Koopman operator in\r\nreproducing kernel
Hilbert spaces, are defined in terms of covariance and\r\ncross-covariance operators
and have been shown to be closely related to the\r\nconditional mean embedding
framework developed by the machine learning\r\ncommunity. The goal of this paper
is to show how the dominant eigenfunctions of\r\nthese operators in combination
with gradient-based optimization techniques can\r\nbe used to detect long-lived
coherent patterns in high-dimensional time-series\r\ndata. The results will be
illustrated using video data and a fluid flow\r\nexample."
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Ingmar
full_name: Schuster, Ingmar
last_name: Schuster
citation:
ama: Klus S, Peitz S, Schuster I. Analyzing high-dimensional time-series data using
kernel transfer operator eigenfunctions. arXiv:180510118. 2018.
apa: Klus, S., Peitz, S., & Schuster, I. (2018). Analyzing high-dimensional
time-series data using kernel transfer operator eigenfunctions. ArXiv:1805.10118.
bibtex: '@article{Klus_Peitz_Schuster_2018, title={Analyzing high-dimensional time-series
data using kernel transfer operator eigenfunctions}, journal={arXiv:1805.10118},
author={Klus, Stefan and Peitz, Sebastian and Schuster, Ingmar}, year={2018} }'
chicago: Klus, Stefan, Sebastian Peitz, and Ingmar Schuster. “Analyzing High-Dimensional
Time-Series Data Using Kernel Transfer Operator Eigenfunctions.” ArXiv:1805.10118,
2018.
ieee: S. Klus, S. Peitz, and I. Schuster, “Analyzing high-dimensional time-series
data using kernel transfer operator eigenfunctions,” arXiv:1805.10118.
2018.
mla: Klus, Stefan, et al. “Analyzing High-Dimensional Time-Series Data Using Kernel
Transfer Operator Eigenfunctions.” ArXiv:1805.10118, 2018.
short: S. Klus, S. Peitz, I. Schuster, ArXiv:1805.10118 (2018).
date_created: 2020-03-13T12:44:12Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/1805.10118.pdf
oa: '1'
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: arXiv:1805.10118
status: public
title: Analyzing high-dimensional time-series data using kernel transfer operator
eigenfunctions
type: preprint
user_id: '47427'
year: '2018'
...
---
_id: '16658'
author:
- first_name: Robert
full_name: Preis, Robert
last_name: Preis
- first_name: Burkhard
full_name: Monien, Burkhard
last_name: Monien
- first_name: Stefan
full_name: Schamberger, Stefan
last_name: Schamberger
citation:
ama: 'Preis R, Monien B, Schamberger S. Approximation Algorithms for Multilevel
Graph Partitioning. In: Handbook of Approximation Algorithms and Metaheuristics.
; 2007. doi:10.1201/9781420010749.ch60'
apa: Preis, R., Monien, B., & Schamberger, S. (2007). Approximation Algorithms
for Multilevel Graph Partitioning. In Handbook of Approximation Algorithms
and Metaheuristics. https://doi.org/10.1201/9781420010749.ch60
bibtex: '@inbook{Preis_Monien_Schamberger_2007, title={Approximation Algorithms
for Multilevel Graph Partitioning}, DOI={10.1201/9781420010749.ch60},
booktitle={Handbook of Approximation Algorithms and Metaheuristics}, author={Preis,
Robert and Monien, Burkhard and Schamberger, Stefan}, year={2007} }'
chicago: Preis, Robert, Burkhard Monien, and Stefan Schamberger. “Approximation
Algorithms for Multilevel Graph Partitioning.” In Handbook of Approximation
Algorithms and Metaheuristics, 2007. https://doi.org/10.1201/9781420010749.ch60.
ieee: R. Preis, B. Monien, and S. Schamberger, “Approximation Algorithms for Multilevel
Graph Partitioning,” in Handbook of Approximation Algorithms and Metaheuristics,
2007.
mla: Preis, Robert, et al. “Approximation Algorithms for Multilevel Graph Partitioning.”
Handbook of Approximation Algorithms and Metaheuristics, 2007, doi:10.1201/9781420010749.ch60.
short: 'R. Preis, B. Monien, S. Schamberger, in: Handbook of Approximation Algorithms
and Metaheuristics, 2007.'
date_created: 2020-04-16T09:33:00Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1201/9781420010749.ch60
language:
- iso: eng
publication: Handbook of Approximation Algorithms and Metaheuristics
publication_identifier:
isbn:
- '9781584885504'
- '9781420010749'
issn:
- 2154-4573
publication_status: published
status: public
title: Approximation Algorithms for Multilevel Graph Partitioning
type: book_chapter
user_id: '15701'
year: '2007'
...
---
_id: '16583'
author:
- first_name: Francois
full_name: Demoures, Francois
last_name: Demoures
- first_name: Francois
full_name: Gay-Balmaz, Francois
last_name: Gay-Balmaz
- first_name: Thomas
full_name: Leitz, Thomas
last_name: Leitz
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Tudor S.
full_name: Ratiu, Tudor S.
last_name: Ratiu
citation:
ama: Demoures F, Gay-Balmaz F, Leitz T, Leyendecker S, Ober-Blöbaum S, Ratiu TS.
Asynchronous variational Lie group integration for geometrically exact beam dynamics.
PAMM. 2013:45-46. doi:10.1002/pamm.201310018
apa: Demoures, F., Gay-Balmaz, F., Leitz, T., Leyendecker, S., Ober-Blöbaum, S.,
& Ratiu, T. S. (2013). Asynchronous variational Lie group integration for
geometrically exact beam dynamics. PAMM, 45–46. https://doi.org/10.1002/pamm.201310018
bibtex: '@article{Demoures_Gay-Balmaz_Leitz_Leyendecker_Ober-Blöbaum_Ratiu_2013,
title={Asynchronous variational Lie group integration for geometrically exact
beam dynamics}, DOI={10.1002/pamm.201310018},
journal={PAMM}, author={Demoures, Francois and Gay-Balmaz, Francois and Leitz,
Thomas and Leyendecker, Sigrid and Ober-Blöbaum, Sina and Ratiu, Tudor S.}, year={2013},
pages={45–46} }'
chicago: Demoures, Francois, Francois Gay-Balmaz, Thomas Leitz, Sigrid Leyendecker,
Sina Ober-Blöbaum, and Tudor S. Ratiu. “Asynchronous Variational Lie Group Integration
for Geometrically Exact Beam Dynamics.” PAMM, 2013, 45–46. https://doi.org/10.1002/pamm.201310018.
ieee: F. Demoures, F. Gay-Balmaz, T. Leitz, S. Leyendecker, S. Ober-Blöbaum, and
T. S. Ratiu, “Asynchronous variational Lie group integration for geometrically
exact beam dynamics,” PAMM, pp. 45–46, 2013.
mla: Demoures, Francois, et al. “Asynchronous Variational Lie Group Integration
for Geometrically Exact Beam Dynamics.” PAMM, 2013, pp. 45–46, doi:10.1002/pamm.201310018.
short: F. Demoures, F. Gay-Balmaz, T. Leitz, S. Leyendecker, S. Ober-Blöbaum, T.S.
Ratiu, PAMM (2013) 45–46.
date_created: 2020-04-16T05:41:52Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1002/pamm.201310018
language:
- iso: eng
page: 45-46
publication: PAMM
publication_identifier:
issn:
- 1617-7061
publication_status: published
status: public
title: Asynchronous variational Lie group integration for geometrically exact beam
dynamics
type: journal_article
user_id: '15701'
year: '2013'
...
---
_id: '21944'
article_number: '044116'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Lorenzo
full_name: Boninsegna, Lorenzo
last_name: Boninsegna
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: Nüske F, Boninsegna L, Clementi C. Coarse-graining molecular systems by spectral
matching. The Journal of Chemical Physics. 2019. doi:10.1063/1.5100131
apa: Nüske, F., Boninsegna, L., & Clementi, C. (2019). Coarse-graining molecular
systems by spectral matching. The Journal of Chemical Physics. https://doi.org/10.1063/1.5100131
bibtex: '@article{Nüske_Boninsegna_Clementi_2019, title={Coarse-graining molecular
systems by spectral matching}, DOI={10.1063/1.5100131},
number={044116}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks
and Boninsegna, Lorenzo and Clementi, Cecilia}, year={2019} }'
chicago: Nüske, Feliks, Lorenzo Boninsegna, and Cecilia Clementi. “Coarse-Graining
Molecular Systems by Spectral Matching.” The Journal of Chemical Physics,
2019. https://doi.org/10.1063/1.5100131.
ieee: F. Nüske, L. Boninsegna, and C. Clementi, “Coarse-graining molecular systems
by spectral matching,” The Journal of Chemical Physics, 2019.
mla: Nüske, Feliks, et al. “Coarse-Graining Molecular Systems by Spectral Matching.”
The Journal of Chemical Physics, 044116, 2019, doi:10.1063/1.5100131.
short: F. Nüske, L. Boninsegna, C. Clementi, The Journal of Chemical Physics (2019).
date_created: 2021-04-30T17:01:13Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.5100131
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
issn:
- 0021-9606
- 1089-7690
publication_status: published
status: public
title: Coarse-graining molecular systems by spectral matching
type: journal_article
user_id: '81513'
year: '2019'
...
---
_id: '17014'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Dellnitz M. Collisions of chaotic attractors. Schlaglichter der Forschung:
Zum 75 Jahrestag der Universität Hamburg. 1994:411-428.'
apa: 'Dellnitz, M. (1994). Collisions of chaotic attractors. Schlaglichter Der
Forschung: Zum 75. Jahrestag Der Universität Hamburg, 411–428.'
bibtex: '@article{Dellnitz_1994, title={Collisions of chaotic attractors}, journal={Schlaglichter
der Forschung: Zum 75. Jahrestag der Universität Hamburg}, author={Dellnitz, Michael},
year={1994}, pages={411–428} }'
chicago: 'Dellnitz, Michael. “Collisions of Chaotic Attractors.” Schlaglichter
Der Forschung: Zum 75. Jahrestag Der Universität Hamburg, 1994, 411–28.'
ieee: 'M. Dellnitz, “Collisions of chaotic attractors,” Schlaglichter der Forschung:
Zum 75. Jahrestag der Universität Hamburg, pp. 411–428, 1994.'
mla: 'Dellnitz, Michael. “Collisions of Chaotic Attractors.” Schlaglichter Der
Forschung: Zum 75. Jahrestag Der Universität Hamburg, 1994, pp. 411–28.'
short: 'M. Dellnitz, Schlaglichter Der Forschung: Zum 75. Jahrestag Der Universität
Hamburg (1994) 411–428.'
date_created: 2020-05-19T09:06:20Z
date_updated: 2022-01-06T06:53:02Z
department:
- _id: '101'
language:
- iso: eng
page: 411-428
publication: 'Schlaglichter der Forschung: Zum 75. Jahrestag der Universität Hamburg'
status: public
title: Collisions of chaotic attractors
type: journal_article
user_id: '32643'
year: '1994'
...
---
_id: '31556'
abstract:
- lang: ger
text: Mehrzieloptimierung behandelt Probleme, bei denen mehrere skalare Zielfunktionen
simultan optimiert werden sollen. Ein Punkt ist in diesem Fall optimal, wenn es
keinen anderen Punkt gibt, der mindestens genauso gut ist in allen Zielfunktionen
und besser in mindestens einer Zielfunktion. Ein notwendiges Optimalitätskriterium
lässt sich über Ableitungsinformationen erster Ordnung der Zielfunktionen herleiten.
Die Menge der Punkte, die dieses notwendige Kriterium erfüllen, wird als Pareto-kritische
Menge bezeichnet. Diese Arbeit enthält neue Resultate über Pareto-kritische Mengen
für glatte und nicht-glatte Mehrzieloptimierungsprobleme, sowohl was deren Berechnung
betrifft als auch deren Struktur. Im glatten Fall erfolgt die Berechnung über
ein Fortsetzungsverfahren, im nichtglatten Fall über ein Abstiegsverfahren. Anschließend
wird die Struktur des Randes der Pareto-kritischen Menge analysiert, welcher aus
Pareto-kritischen Mengen kleinerer Subprobleme besteht. Schlussendlich werden
inverse Probleme betrachtet, bei denen zu einer gegebenen Datenmenge ein Zielfunktionsvektor
gefunden werden soll, für den die Datenpunkte kritisch sind.
- lang: eng
text: Multiobjective optimization is concerned with the simultaneous optimization
of multiple scalar-valued functions. In this case, a point is optimal if there
is no other point that is at least as good in all objectives and better in at
least one objective. A necessary condition for optimality can be derived based
on first-order information of the objectives. The set of points that satisfy this
necessary condition is called the Pareto critical set. This thesis presents new
results about Pareto critical sets for smooth and nonsmooth multiobjective optimization
problems, both in terms of their efficient computation and structural properties.
In the smooth case they are computed via a continuation method and in the nonsmooth
case via a descent method. Afterwards, the structure of the boundary of the Pareto
critical set is analyzed, which consists of Pareto critical sets of smaller subproblems.
Finally, inverse problems are considered, where a data set is given and an objective
vector is sought for which the data points are critical.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
citation:
ama: Gebken B. Computation and Analysis of Pareto Critical Sets in Smooth and
Nonsmooth Multiobjective Optimization.; 2022. doi:10.17619/UNIPB/1-1327
apa: Gebken, B. (2022). Computation and analysis of Pareto critical sets in smooth
and nonsmooth multiobjective optimization. https://doi.org/10.17619/UNIPB/1-1327
bibtex: '@book{Gebken_2022, title={Computation and analysis of Pareto critical sets
in smooth and nonsmooth multiobjective optimization}, DOI={10.17619/UNIPB/1-1327},
author={Gebken, Bennet}, year={2022} }'
chicago: Gebken, Bennet. Computation and Analysis of Pareto Critical Sets in
Smooth and Nonsmooth Multiobjective Optimization, 2022. https://doi.org/10.17619/UNIPB/1-1327.
ieee: B. Gebken, Computation and analysis of Pareto critical sets in smooth and
nonsmooth multiobjective optimization. 2022.
mla: Gebken, Bennet. Computation and Analysis of Pareto Critical Sets in Smooth
and Nonsmooth Multiobjective Optimization. 2022, doi:10.17619/UNIPB/1-1327.
short: B. Gebken, Computation and Analysis of Pareto Critical Sets in Smooth and
Nonsmooth Multiobjective Optimization, 2022.
date_created: 2022-06-01T06:48:08Z
date_updated: 2022-06-01T07:13:09Z
department:
- _id: '101'
doi: 10.17619/UNIPB/1-1327
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://digital.ub.uni-paderborn.de/hs/download/pdf/6531779
oa: '1'
status: public
supervisor:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
title: Computation and analysis of Pareto critical sets in smooth and nonsmooth multiobjective
optimization
type: dissertation
user_id: '32643'
year: '2022'
...
---
_id: '16584'
author:
- first_name: Peter
full_name: Deuflhard, Peter
last_name: Deuflhard
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Christof
full_name: Schütte, Christof
last_name: Schütte
citation:
ama: 'Deuflhard P, Dellnitz M, Junge O, Schütte C. Computation of Essential Molecular
Dynamics by Subdivision Techniques. In: Computational Molecular Dynamics: Challenges,
Methods, Ideas. Berlin, Heidelberg; 1999. doi:10.1007/978-3-642-58360-5_5'
apa: 'Deuflhard, P., Dellnitz, M., Junge, O., & Schütte, C. (1999). Computation
of Essential Molecular Dynamics by Subdivision Techniques. In Computational
Molecular Dynamics: Challenges, Methods, Ideas. Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58360-5_5'
bibtex: '@inbook{Deuflhard_Dellnitz_Junge_Schütte_1999, place={Berlin, Heidelberg},
title={Computation of Essential Molecular Dynamics by Subdivision Techniques},
DOI={10.1007/978-3-642-58360-5_5},
booktitle={Computational Molecular Dynamics: Challenges, Methods, Ideas}, author={Deuflhard,
Peter and Dellnitz, Michael and Junge, Oliver and Schütte, Christof}, year={1999}
}'
chicago: 'Deuflhard, Peter, Michael Dellnitz, Oliver Junge, and Christof Schütte.
“Computation of Essential Molecular Dynamics by Subdivision Techniques.” In Computational
Molecular Dynamics: Challenges, Methods, Ideas. Berlin, Heidelberg, 1999.
https://doi.org/10.1007/978-3-642-58360-5_5.'
ieee: 'P. Deuflhard, M. Dellnitz, O. Junge, and C. Schütte, “Computation of Essential
Molecular Dynamics by Subdivision Techniques,” in Computational Molecular Dynamics:
Challenges, Methods, Ideas, Berlin, Heidelberg, 1999.'
mla: 'Deuflhard, Peter, et al. “Computation of Essential Molecular Dynamics by Subdivision
Techniques.” Computational Molecular Dynamics: Challenges, Methods, Ideas,
1999, doi:10.1007/978-3-642-58360-5_5.'
short: 'P. Deuflhard, M. Dellnitz, O. Junge, C. Schütte, in: Computational Molecular
Dynamics: Challenges, Methods, Ideas, Berlin, Heidelberg, 1999.'
date_created: 2020-04-16T05:43:16Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-3-642-58360-5_5
language:
- iso: eng
place: Berlin, Heidelberg
publication: 'Computational Molecular Dynamics: Challenges, Methods, Ideas'
publication_identifier:
isbn:
- '9783540632429'
- '9783642583605'
issn:
- 1439-7358
publication_status: published
status: public
title: Computation of Essential Molecular Dynamics by Subdivision Techniques
type: book_chapter
user_id: '15701'
year: '1999'
...
---
_id: '16545'
article_number: '243'
author:
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
- first_name: K.
full_name: Witting, K.
last_name: Witting
citation:
ama: Dellnitz M, Witting K. Computation of robust Pareto points. International
Journal of Computing Science and Mathematics. 2009. doi:10.1504/ijcsm.2009.027876
apa: Dellnitz, M., & Witting, K. (2009). Computation of robust Pareto points.
International Journal of Computing Science and Mathematics. https://doi.org/10.1504/ijcsm.2009.027876
bibtex: '@article{Dellnitz_Witting_2009, title={Computation of robust Pareto points},
DOI={10.1504/ijcsm.2009.027876},
number={243}, journal={International Journal of Computing Science and Mathematics},
author={Dellnitz, M. and Witting, K.}, year={2009} }'
chicago: Dellnitz, M., and K. Witting. “Computation of Robust Pareto Points.” International
Journal of Computing Science and Mathematics, 2009. https://doi.org/10.1504/ijcsm.2009.027876.
ieee: M. Dellnitz and K. Witting, “Computation of robust Pareto points,” International
Journal of Computing Science and Mathematics, 2009.
mla: Dellnitz, M., and K. Witting. “Computation of Robust Pareto Points.” International
Journal of Computing Science and Mathematics, 243, 2009, doi:10.1504/ijcsm.2009.027876.
short: M. Dellnitz, K. Witting, International Journal of Computing Science and Mathematics
(2009).
date_created: 2020-04-15T08:54:35Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1504/ijcsm.2009.027876
language:
- iso: eng
publication: International Journal of Computing Science and Mathematics
publication_identifier:
issn:
- 1752-5055
- 1752-5063
publication_status: published
status: public
title: Computation of robust Pareto points
type: journal_article
user_id: '15701'
year: '2009'
...
---
_id: '16498'
author:
- first_name: P. J.
full_name: Aston, P. J.
last_name: Aston
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
citation:
ama: 'Aston PJ, Dellnitz M. Computation of the dominant Lyapunov exponent via spatial
integration using matrix norms. Proceedings of the Royal Society of London
Series A: Mathematical, Physical and Engineering Sciences. 2003:2933-2955.
doi:10.1098/rspa.2003.1143'
apa: 'Aston, P. J., & Dellnitz, M. (2003). Computation of the dominant Lyapunov
exponent via spatial integration using matrix norms. Proceedings of the Royal
Society of London. Series A: Mathematical, Physical and Engineering Sciences,
2933–2955. https://doi.org/10.1098/rspa.2003.1143'
bibtex: '@article{Aston_Dellnitz_2003, title={Computation of the dominant Lyapunov
exponent via spatial integration using matrix norms}, DOI={10.1098/rspa.2003.1143},
journal={Proceedings of the Royal Society of London. Series A: Mathematical, Physical
and Engineering Sciences}, author={Aston, P. J. and Dellnitz, M.}, year={2003},
pages={2933–2955} }'
chicago: 'Aston, P. J., and M. Dellnitz. “Computation of the Dominant Lyapunov Exponent
via Spatial Integration Using Matrix Norms.” Proceedings of the Royal Society
of London. Series A: Mathematical, Physical and Engineering Sciences, 2003,
2933–55. https://doi.org/10.1098/rspa.2003.1143.'
ieee: 'P. J. Aston and M. Dellnitz, “Computation of the dominant Lyapunov exponent
via spatial integration using matrix norms,” Proceedings of the Royal Society
of London. Series A: Mathematical, Physical and Engineering Sciences, pp.
2933–2955, 2003.'
mla: 'Aston, P. J., and M. Dellnitz. “Computation of the Dominant Lyapunov Exponent
via Spatial Integration Using Matrix Norms.” Proceedings of the Royal Society
of London. Series A: Mathematical, Physical and Engineering Sciences, 2003,
pp. 2933–55, doi:10.1098/rspa.2003.1143.'
short: 'P.J. Aston, M. Dellnitz, Proceedings of the Royal Society of London. Series
A: Mathematical, Physical and Engineering Sciences (2003) 2933–2955.'
date_created: 2020-04-14T09:57:39Z
date_updated: 2022-01-06T06:52:51Z
department:
- _id: '101'
doi: 10.1098/rspa.2003.1143
language:
- iso: eng
page: 2933-2955
publication: 'Proceedings of the Royal Society of London. Series A: Mathematical,
Physical and Engineering Sciences'
publication_identifier:
issn:
- 1364-5021
- 1471-2946
publication_status: published
status: public
title: Computation of the dominant Lyapunov exponent via spatial integration using
matrix norms
type: journal_article
user_id: '47427'
year: '2003'
...
---
_id: '17012'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Dellnitz M. Computational bifurcation of periodic solutions in systems with
symmetry. IMA Journal of Numerical Analysis. 1992;12(3):429-455. doi:10.1093/imanum/12.3.429
apa: Dellnitz, M. (1992). Computational bifurcation of periodic solutions in systems
with symmetry. IMA Journal of Numerical Analysis, 12(3), 429–455.
https://doi.org/10.1093/imanum/12.3.429
bibtex: '@article{Dellnitz_1992, title={Computational bifurcation of periodic solutions
in systems with symmetry}, volume={12}, DOI={10.1093/imanum/12.3.429},
number={3}, journal={IMA Journal of Numerical Analysis}, author={Dellnitz, Michael},
year={1992}, pages={429–455} }'
chicago: 'Dellnitz, Michael. “Computational Bifurcation of Periodic Solutions in
Systems with Symmetry.” IMA Journal of Numerical Analysis 12, no. 3 (1992):
429–55. https://doi.org/10.1093/imanum/12.3.429.'
ieee: M. Dellnitz, “Computational bifurcation of periodic solutions in systems with
symmetry,” IMA Journal of Numerical Analysis, vol. 12, no. 3, pp. 429–455,
1992.
mla: Dellnitz, Michael. “Computational Bifurcation of Periodic Solutions in Systems
with Symmetry.” IMA Journal of Numerical Analysis, vol. 12, no. 3, 1992,
pp. 429–55, doi:10.1093/imanum/12.3.429.
short: M. Dellnitz, IMA Journal of Numerical Analysis 12 (1992) 429–455.
date_created: 2020-05-19T08:53:14Z
date_updated: 2022-01-06T06:53:02Z
department:
- _id: '101'
doi: 10.1093/imanum/12.3.429
intvolume: ' 12'
issue: '3'
language:
- iso: eng
page: 429-455
publication: IMA Journal of Numerical Analysis
publication_status: published
status: public
title: Computational bifurcation of periodic solutions in systems with symmetry
type: journal_article
user_id: '32643'
volume: 12
year: '1992'
...
---
_id: '16682'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Bodo
full_name: Werner, Bodo
last_name: Werner
citation:
ama: Dellnitz M, Werner B. Computational methods for bifurcation problems with symmetries—with
special attention to steady state and Hopf bifurcation points. Journal of Computational
and Applied Mathematics. 1989:97-123. doi:10.1016/0377-0427(89)90150-7
apa: Dellnitz, M., & Werner, B. (1989). Computational methods for bifurcation
problems with symmetries—with special attention to steady state and Hopf bifurcation
points. Journal of Computational and Applied Mathematics, 97–123. https://doi.org/10.1016/0377-0427(89)90150-7
bibtex: '@article{Dellnitz_Werner_1989, title={Computational methods for bifurcation
problems with symmetries—with special attention to steady state and Hopf bifurcation
points}, DOI={10.1016/0377-0427(89)90150-7},
journal={Journal of Computational and Applied Mathematics}, author={Dellnitz,
Michael and Werner, Bodo}, year={1989}, pages={97–123} }'
chicago: Dellnitz, Michael, and Bodo Werner. “Computational Methods for Bifurcation
Problems with Symmetries—with Special Attention to Steady State and Hopf Bifurcation
Points.” Journal of Computational and Applied Mathematics, 1989, 97–123.
https://doi.org/10.1016/0377-0427(89)90150-7.
ieee: M. Dellnitz and B. Werner, “Computational methods for bifurcation problems
with symmetries—with special attention to steady state and Hopf bifurcation points,”
Journal of Computational and Applied Mathematics, pp. 97–123, 1989.
mla: Dellnitz, Michael, and Bodo Werner. “Computational Methods for Bifurcation
Problems with Symmetries—with Special Attention to Steady State and Hopf Bifurcation
Points.” Journal of Computational and Applied Mathematics, 1989, pp. 97–123,
doi:10.1016/0377-0427(89)90150-7.
short: M. Dellnitz, B. Werner, Journal of Computational and Applied Mathematics
(1989) 97–123.
date_created: 2020-04-16T10:28:09Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1016/0377-0427(89)90150-7
language:
- iso: eng
page: 97-123
publication: Journal of Computational and Applied Mathematics
publication_identifier:
issn:
- 0377-0427
publication_status: published
status: public
title: Computational methods for bifurcation problems with symmetries—with special
attention to steady state and Hopf bifurcation points
type: journal_article
user_id: '15701'
year: '1989'
...
---
_id: '16608'
author:
- first_name: Tobias
full_name: Gail, Tobias
last_name: Gail
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
citation:
ama: Gail T, Leyendecker S, Ober-Blöbaum S. Computing time investigations for variational
multirate integration. PAMM. 2013:43-44. doi:10.1002/pamm.201310017
apa: Gail, T., Leyendecker, S., & Ober-Blöbaum, S. (2013). Computing time investigations
for variational multirate integration. PAMM, 43–44. https://doi.org/10.1002/pamm.201310017
bibtex: '@article{Gail_Leyendecker_Ober-Blöbaum_2013, title={Computing time investigations
for variational multirate integration}, DOI={10.1002/pamm.201310017},
journal={PAMM}, author={Gail, Tobias and Leyendecker, Sigrid and Ober-Blöbaum,
Sina}, year={2013}, pages={43–44} }'
chicago: Gail, Tobias, Sigrid Leyendecker, and Sina Ober-Blöbaum. “Computing Time
Investigations for Variational Multirate Integration.” PAMM, 2013, 43–44.
https://doi.org/10.1002/pamm.201310017.
ieee: T. Gail, S. Leyendecker, and S. Ober-Blöbaum, “Computing time investigations
for variational multirate integration,” PAMM, pp. 43–44, 2013.
mla: Gail, Tobias, et al. “Computing Time Investigations for Variational Multirate
Integration.” PAMM, 2013, pp. 43–44, doi:10.1002/pamm.201310017.
short: T. Gail, S. Leyendecker, S. Ober-Blöbaum, PAMM (2013) 43–44.
date_created: 2020-04-16T07:58:09Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1002/pamm.201310017
language:
- iso: eng
page: 43-44
publication: PAMM
publication_identifier:
issn:
- 1617-7061
publication_status: published
status: public
title: Computing time investigations for variational multirate integration
type: journal_article
user_id: '15701'
year: '2013'
...
---
_id: '16543'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Robert
full_name: Preis, Robert
last_name: Preis
citation:
ama: 'Dellnitz M, Preis R. Congestion and Almost Invariant Sets in Dynamical Systems.
In: Lecture Notes in Computer Science. Berlin, Heidelberg; 2003. doi:10.1007/3-540-45084-x_8'
apa: Dellnitz, M., & Preis, R. (2003). Congestion and Almost Invariant Sets
in Dynamical Systems. In Lecture Notes in Computer Science. Berlin, Heidelberg.
https://doi.org/10.1007/3-540-45084-x_8
bibtex: '@inbook{Dellnitz_Preis_2003, place={Berlin, Heidelberg}, title={Congestion
and Almost Invariant Sets in Dynamical Systems}, DOI={10.1007/3-540-45084-x_8},
booktitle={Lecture Notes in Computer Science}, author={Dellnitz, Michael and Preis,
Robert}, year={2003} }'
chicago: Dellnitz, Michael, and Robert Preis. “Congestion and Almost Invariant Sets
in Dynamical Systems.” In Lecture Notes in Computer Science. Berlin, Heidelberg,
2003. https://doi.org/10.1007/3-540-45084-x_8.
ieee: M. Dellnitz and R. Preis, “Congestion and Almost Invariant Sets in Dynamical
Systems,” in Lecture Notes in Computer Science, Berlin, Heidelberg, 2003.
mla: Dellnitz, Michael, and Robert Preis. “Congestion and Almost Invariant Sets
in Dynamical Systems.” Lecture Notes in Computer Science, 2003, doi:10.1007/3-540-45084-x_8.
short: 'M. Dellnitz, R. Preis, in: Lecture Notes in Computer Science, Berlin, Heidelberg,
2003.'
date_created: 2020-04-15T08:50:07Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/3-540-45084-x_8
language:
- iso: eng
place: Berlin, Heidelberg
publication: Lecture Notes in Computer Science
publication_identifier:
isbn:
- '9783540405542'
- '9783540450849'
issn:
- 0302-9743
publication_status: published
status: public
title: Congestion and Almost Invariant Sets in Dynamical Systems
type: book_chapter
user_id: '15701'
year: '2003'
...
---
_id: '16575'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Kathrin
full_name: Padberg, Kathrin
last_name: Padberg
- first_name: Robert
full_name: Preis, Robert
last_name: Preis
- first_name: Bianca
full_name: Thiere, Bianca
last_name: Thiere
citation:
ama: 'Dellnitz M, Padberg K, Preis R, Thiere B. Continuous and Discrete Concepts
for Detecting Transport Barriers in the Planar Circular Restricted Three Body
Problem. In: Nonlinear Science and Complexity. Dordrecht; 2010. doi:10.1007/978-90-481-9884-9_12'
apa: Dellnitz, M., Padberg, K., Preis, R., & Thiere, B. (2010). Continuous and
Discrete Concepts for Detecting Transport Barriers in the Planar Circular Restricted
Three Body Problem. In Nonlinear Science and Complexity. Dordrecht. https://doi.org/10.1007/978-90-481-9884-9_12
bibtex: '@inbook{Dellnitz_Padberg_Preis_Thiere_2010, place={Dordrecht}, title={Continuous
and Discrete Concepts for Detecting Transport Barriers in the Planar Circular
Restricted Three Body Problem}, DOI={10.1007/978-90-481-9884-9_12},
booktitle={Nonlinear Science and Complexity}, author={Dellnitz, Michael and Padberg,
Kathrin and Preis, Robert and Thiere, Bianca}, year={2010} }'
chicago: Dellnitz, Michael, Kathrin Padberg, Robert Preis, and Bianca Thiere. “Continuous
and Discrete Concepts for Detecting Transport Barriers in the Planar Circular
Restricted Three Body Problem.” In Nonlinear Science and Complexity. Dordrecht,
2010. https://doi.org/10.1007/978-90-481-9884-9_12.
ieee: M. Dellnitz, K. Padberg, R. Preis, and B. Thiere, “Continuous and Discrete
Concepts for Detecting Transport Barriers in the Planar Circular Restricted Three
Body Problem,” in Nonlinear Science and Complexity, Dordrecht, 2010.
mla: Dellnitz, Michael, et al. “Continuous and Discrete Concepts for Detecting Transport
Barriers in the Planar Circular Restricted Three Body Problem.” Nonlinear Science
and Complexity, 2010, doi:10.1007/978-90-481-9884-9_12.
short: 'M. Dellnitz, K. Padberg, R. Preis, B. Thiere, in: Nonlinear Science and
Complexity, Dordrecht, 2010.'
date_created: 2020-04-16T05:06:58Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-90-481-9884-9_12
place: Dordrecht
publication: Nonlinear Science and Complexity
publication_identifier:
isbn:
- '9789048198832'
- '9789048198849'
publication_status: published
status: public
title: Continuous and Discrete Concepts for Detecting Transport Barriers in the Planar
Circular Restricted Three Body Problem
type: book_chapter
user_id: '15701'
year: '2010'
...
---
_id: '16709'
author:
- first_name: Tuhin
full_name: Sahai, Tuhin
last_name: Sahai
- first_name: Adrian
full_name: Ziessler, Adrian
last_name: Ziessler
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Sahai T, Ziessler A, Klus S, Dellnitz M. Continuous relaxations for the traveling
salesman problem. Nonlinear Dynamics. 2019. doi:10.1007/s11071-019-05092-5
apa: Sahai, T., Ziessler, A., Klus, S., & Dellnitz, M. (2019). Continuous relaxations
for the traveling salesman problem. Nonlinear Dynamics. https://doi.org/10.1007/s11071-019-05092-5
bibtex: '@article{Sahai_Ziessler_Klus_Dellnitz_2019, title={Continuous relaxations
for the traveling salesman problem}, DOI={10.1007/s11071-019-05092-5},
journal={Nonlinear Dynamics}, author={Sahai, Tuhin and Ziessler, Adrian and Klus,
Stefan and Dellnitz, Michael}, year={2019} }'
chicago: Sahai, Tuhin, Adrian Ziessler, Stefan Klus, and Michael Dellnitz. “Continuous
Relaxations for the Traveling Salesman Problem.” Nonlinear Dynamics, 2019.
https://doi.org/10.1007/s11071-019-05092-5.
ieee: T. Sahai, A. Ziessler, S. Klus, and M. Dellnitz, “Continuous relaxations for
the traveling salesman problem,” Nonlinear Dynamics, 2019.
mla: Sahai, Tuhin, et al. “Continuous Relaxations for the Traveling Salesman Problem.”
Nonlinear Dynamics, 2019, doi:10.1007/s11071-019-05092-5.
short: T. Sahai, A. Ziessler, S. Klus, M. Dellnitz, Nonlinear Dynamics (2019).
date_created: 2020-04-16T14:05:04Z
date_updated: 2022-01-06T06:52:55Z
department:
- _id: '101'
doi: 10.1007/s11071-019-05092-5
language:
- iso: eng
publication: Nonlinear Dynamics
publication_identifier:
issn:
- 0924-090X
- 1573-269X
publication_status: published
status: public
title: Continuous relaxations for the traveling salesman problem
type: journal_article
user_id: '47427'
year: '2019'
...
---
_id: '16597'
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Julia
full_name: Timmermann, Julia
last_name: Timmermann
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Ansgar
full_name: Trächtler, Ansgar
last_name: Trächtler
citation:
ama: Flaßkamp K, Timmermann J, Ober-Blöbaum S, Trächtler A. Control strategies on
stable manifolds for energy-efficient swing-ups of double pendula. International
Journal of Control. 2014:1886-1905. doi:10.1080/00207179.2014.893450
apa: Flaßkamp, K., Timmermann, J., Ober-Blöbaum, S., & Trächtler, A. (2014).
Control strategies on stable manifolds for energy-efficient swing-ups of double
pendula. International Journal of Control, 1886–1905. https://doi.org/10.1080/00207179.2014.893450
bibtex: '@article{Flaßkamp_Timmermann_Ober-Blöbaum_Trächtler_2014, title={Control
strategies on stable manifolds for energy-efficient swing-ups of double pendula},
DOI={10.1080/00207179.2014.893450},
journal={International Journal of Control}, author={Flaßkamp, Kathrin and Timmermann,
Julia and Ober-Blöbaum, Sina and Trächtler, Ansgar}, year={2014}, pages={1886–1905}
}'
chicago: Flaßkamp, Kathrin, Julia Timmermann, Sina Ober-Blöbaum, and Ansgar Trächtler.
“Control Strategies on Stable Manifolds for Energy-Efficient Swing-Ups of Double
Pendula.” International Journal of Control, 2014, 1886–1905. https://doi.org/10.1080/00207179.2014.893450.
ieee: K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, and A. Trächtler, “Control strategies
on stable manifolds for energy-efficient swing-ups of double pendula,” International
Journal of Control, pp. 1886–1905, 2014.
mla: Flaßkamp, Kathrin, et al. “Control Strategies on Stable Manifolds for Energy-Efficient
Swing-Ups of Double Pendula.” International Journal of Control, 2014, pp.
1886–905, doi:10.1080/00207179.2014.893450.
short: K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, A. Trächtler, International
Journal of Control (2014) 1886–1905.
date_created: 2020-04-16T06:00:59Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1080/00207179.2014.893450
language:
- iso: eng
page: 1886-1905
publication: International Journal of Control
publication_identifier:
issn:
- 0020-7179
- 1366-5820
publication_status: published
status: public
title: Control strategies on stable manifolds for energy-efficient swing-ups of double
pendula
type: journal_article
user_id: '15701'
year: '2014'
...
---
_id: '16292'
abstract:
- lang: eng
text: "In a recent article, we presented a framework to control nonlinear partial\r\ndifferential
equations (PDEs) by means of Koopman operator based reduced models\r\nand concepts
from switched systems. The main idea was to transform a control\r\nsystem into
a set of autonomous systems for which the optimal switching\r\nsequence has to
be computed. These individual systems can be approximated very\r\nefficiently
by reduced order models obtained from data, and one can guarantee\r\nequality
of the full and the reduced objective function under certain\r\nassumptions. In
this article, we extend these results to continuous control\r\ninputs using convex
combinations of multiple Koopman operators corresponding to\r\nconstant controls,
which results in a bilinear control system. Although\r\nequality of the objectives
can be carried over when the PDE depends linearly on\r\nthe control, we show that
this approach is also valid in other scenarios using\r\nseveral flow control examples
of varying complexity."
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: Peitz S. Controlling nonlinear PDEs using low-dimensional bilinear approximations
obtained from data. arXiv:180106419. 2018.
apa: Peitz, S. (2018). Controlling nonlinear PDEs using low-dimensional bilinear
approximations obtained from data. ArXiv:1801.06419.
bibtex: '@article{Peitz_2018, title={Controlling nonlinear PDEs using low-dimensional
bilinear approximations obtained from data}, journal={arXiv:1801.06419}, author={Peitz,
Sebastian}, year={2018} }'
chicago: Peitz, Sebastian. “Controlling Nonlinear PDEs Using Low-Dimensional Bilinear
Approximations Obtained from Data.” ArXiv:1801.06419, 2018.
ieee: S. Peitz, “Controlling nonlinear PDEs using low-dimensional bilinear approximations
obtained from data,” arXiv:1801.06419. 2018.
mla: Peitz, Sebastian. “Controlling Nonlinear PDEs Using Low-Dimensional Bilinear
Approximations Obtained from Data.” ArXiv:1801.06419, 2018.
short: S. Peitz, ArXiv:1801.06419 (2018).
date_created: 2020-03-13T12:43:14Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/1801.06419.pdf
oa: '1'
publication: arXiv:1801.06419
status: public
title: Controlling nonlinear PDEs using low-dimensional bilinear approximations obtained
from data
type: preprint
user_id: '47427'
year: '2018'
...
---
_id: '16668'
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Marco
full_name: Laumanns, Marco
last_name: Laumanns
- first_name: Carlos A.
full_name: Coello Coello, Carlos A.
last_name: Coello Coello
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: El-Ghazali
full_name: Talbi, El-Ghazali
last_name: Talbi
citation:
ama: Schütze O, Laumanns M, Coello Coello CA, Dellnitz M, Talbi E-G. Convergence
of stochastic search algorithms to finite size pareto set approximations. Journal
of Global Optimization. 2008:559-577. doi:10.1007/s10898-007-9265-7
apa: Schütze, O., Laumanns, M., Coello Coello, C. A., Dellnitz, M., & Talbi,
E.-G. (2008). Convergence of stochastic search algorithms to finite size pareto
set approximations. Journal of Global Optimization, 559–577. https://doi.org/10.1007/s10898-007-9265-7
bibtex: '@article{Schütze_Laumanns_Coello Coello_Dellnitz_Talbi_2008, title={Convergence
of stochastic search algorithms to finite size pareto set approximations}, DOI={10.1007/s10898-007-9265-7},
journal={Journal of Global Optimization}, author={Schütze, Oliver and Laumanns,
Marco and Coello Coello, Carlos A. and Dellnitz, Michael and Talbi, El-Ghazali},
year={2008}, pages={559–577} }'
chicago: Schütze, Oliver, Marco Laumanns, Carlos A. Coello Coello, Michael Dellnitz,
and El-Ghazali Talbi. “Convergence of Stochastic Search Algorithms to Finite Size
Pareto Set Approximations.” Journal of Global Optimization, 2008, 559–77.
https://doi.org/10.1007/s10898-007-9265-7.
ieee: O. Schütze, M. Laumanns, C. A. Coello Coello, M. Dellnitz, and E.-G. Talbi,
“Convergence of stochastic search algorithms to finite size pareto set approximations,”
Journal of Global Optimization, pp. 559–577, 2008.
mla: Schütze, Oliver, et al. “Convergence of Stochastic Search Algorithms to Finite
Size Pareto Set Approximations.” Journal of Global Optimization, 2008,
pp. 559–77, doi:10.1007/s10898-007-9265-7.
short: O. Schütze, M. Laumanns, C.A. Coello Coello, M. Dellnitz, E.-G. Talbi, Journal
of Global Optimization (2008) 559–577.
date_created: 2020-04-16T10:02:17Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/s10898-007-9265-7
language:
- iso: eng
page: 559-577
publication: Journal of Global Optimization
publication_identifier:
issn:
- 0925-5001
- 1573-2916
publication_status: published
status: public
title: Convergence of stochastic search algorithms to finite size pareto set approximations
type: journal_article
user_id: '15701'
year: '2008'
...
---
_id: '16665'
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Sanaz
full_name: Mostaghim, Sanaz
last_name: Mostaghim
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Jürgen
full_name: Teich, Jürgen
last_name: Teich
citation:
ama: 'Schütze O, Mostaghim S, Dellnitz M, Teich J. Covering Pareto Sets by Multilevel
Evolutionary Subdivision Techniques. In: Lecture Notes in Computer Science.
Berlin, Heidelberg; 2003. doi:10.1007/3-540-36970-8_9'
apa: Schütze, O., Mostaghim, S., Dellnitz, M., & Teich, J. (2003). Covering
Pareto Sets by Multilevel Evolutionary Subdivision Techniques. In Lecture Notes
in Computer Science. Berlin, Heidelberg. https://doi.org/10.1007/3-540-36970-8_9
bibtex: '@inbook{Schütze_Mostaghim_Dellnitz_Teich_2003, place={Berlin, Heidelberg},
title={Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques},
DOI={10.1007/3-540-36970-8_9},
booktitle={Lecture Notes in Computer Science}, author={Schütze, Oliver and Mostaghim,
Sanaz and Dellnitz, Michael and Teich, Jürgen}, year={2003} }'
chicago: Schütze, Oliver, Sanaz Mostaghim, Michael Dellnitz, and Jürgen Teich. “Covering
Pareto Sets by Multilevel Evolutionary Subdivision Techniques.” In Lecture
Notes in Computer Science. Berlin, Heidelberg, 2003. https://doi.org/10.1007/3-540-36970-8_9.
ieee: O. Schütze, S. Mostaghim, M. Dellnitz, and J. Teich, “Covering Pareto Sets
by Multilevel Evolutionary Subdivision Techniques,” in Lecture Notes in Computer
Science, Berlin, Heidelberg, 2003.
mla: Schütze, Oliver, et al. “Covering Pareto Sets by Multilevel Evolutionary Subdivision
Techniques.” Lecture Notes in Computer Science, 2003, doi:10.1007/3-540-36970-8_9.
short: 'O. Schütze, S. Mostaghim, M. Dellnitz, J. Teich, in: Lecture Notes in Computer
Science, Berlin, Heidelberg, 2003.'
date_created: 2020-04-16T09:58:10Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/3-540-36970-8_9
language:
- iso: eng
place: Berlin, Heidelberg
publication: Lecture Notes in Computer Science
publication_identifier:
isbn:
- '9783540018698'
- '9783540369707'
issn:
- 0302-9743
publication_status: published
status: public
title: Covering Pareto Sets by Multilevel Evolutionary Subdivision Techniques
type: book_chapter
user_id: '15701'
year: '2003'
...
---
_id: '16684'
author:
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
- first_name: O.
full_name: Sch�tze, O.
last_name: Sch�tze
- first_name: T.
full_name: Hestermeyer, T.
last_name: Hestermeyer
citation:
ama: Dellnitz M, Sch�tze O, Hestermeyer T. Covering Pareto Sets by Multilevel Subdivision
Techniques. Journal of Optimization Theory and Applications. 2005:113-136.
doi:10.1007/s10957-004-6468-7
apa: Dellnitz, M., Sch�tze, O., & Hestermeyer, T. (2005). Covering Pareto Sets
by Multilevel Subdivision Techniques. Journal of Optimization Theory and Applications,
113–136. https://doi.org/10.1007/s10957-004-6468-7
bibtex: '@article{Dellnitz_Sch�tze_Hestermeyer_2005, title={Covering Pareto Sets
by Multilevel Subdivision Techniques}, DOI={10.1007/s10957-004-6468-7},
journal={Journal of Optimization Theory and Applications}, author={Dellnitz, M.
and Sch�tze, O. and Hestermeyer, T.}, year={2005}, pages={113–136} }'
chicago: Dellnitz, M., O. Sch�tze, and T. Hestermeyer. “Covering Pareto Sets by
Multilevel Subdivision Techniques.” Journal of Optimization Theory and Applications,
2005, 113–36. https://doi.org/10.1007/s10957-004-6468-7.
ieee: M. Dellnitz, O. Sch�tze, and T. Hestermeyer, “Covering Pareto Sets by Multilevel
Subdivision Techniques,” Journal of Optimization Theory and Applications,
pp. 113–136, 2005.
mla: Dellnitz, M., et al. “Covering Pareto Sets by Multilevel Subdivision Techniques.”
Journal of Optimization Theory and Applications, 2005, pp. 113–36, doi:10.1007/s10957-004-6468-7.
short: M. Dellnitz, O. Sch�tze, T. Hestermeyer, Journal of Optimization Theory and
Applications (2005) 113–136.
date_created: 2020-04-16T10:31:32Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/s10957-004-6468-7
language:
- iso: eng
page: 113-136
publication: Journal of Optimization Theory and Applications
publication_identifier:
issn:
- 0022-3239
- 1573-2878
publication_status: published
status: public
title: Covering Pareto Sets by Multilevel Subdivision Techniques
type: journal_article
user_id: '15701'
year: '2005'
...
---
_id: '16550'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Michael
full_name: Field, Michael
last_name: Field
- first_name: Martin
full_name: Golubitsky, Martin
last_name: Golubitsky
- first_name: Jun
full_name: Ma, Jun
last_name: Ma
- first_name: Andreas
full_name: Hohmann, Andreas
last_name: Hohmann
citation:
ama: Dellnitz M, Field M, Golubitsky M, Ma J, Hohmann A. Cycling Chaos. International
Journal of Bifurcation and Chaos. 1995:1243-1247. doi:10.1142/s0218127495000909
apa: Dellnitz, M., Field, M., Golubitsky, M., Ma, J., & Hohmann, A. (1995).
Cycling Chaos. International Journal of Bifurcation and Chaos, 1243–1247.
https://doi.org/10.1142/s0218127495000909
bibtex: '@article{Dellnitz_Field_Golubitsky_Ma_Hohmann_1995, title={Cycling Chaos},
DOI={10.1142/s0218127495000909},
journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael
and Field, Michael and Golubitsky, Martin and Ma, Jun and Hohmann, Andreas}, year={1995},
pages={1243–1247} }'
chicago: Dellnitz, Michael, Michael Field, Martin Golubitsky, Jun Ma, and Andreas
Hohmann. “Cycling Chaos.” International Journal of Bifurcation and Chaos,
1995, 1243–47. https://doi.org/10.1142/s0218127495000909.
ieee: M. Dellnitz, M. Field, M. Golubitsky, J. Ma, and A. Hohmann, “Cycling Chaos,”
International Journal of Bifurcation and Chaos, pp. 1243–1247, 1995.
mla: Dellnitz, Michael, et al. “Cycling Chaos.” International Journal of Bifurcation
and Chaos, 1995, pp. 1243–47, doi:10.1142/s0218127495000909.
short: M. Dellnitz, M. Field, M. Golubitsky, J. Ma, A. Hohmann, International Journal
of Bifurcation and Chaos (1995) 1243–1247.
date_created: 2020-04-15T09:04:16Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1142/s0218127495000909
language:
- iso: eng
page: 1243-1247
publication: International Journal of Bifurcation and Chaos
publication_identifier:
issn:
- 0218-1274
- 1793-6551
publication_status: published
status: public
title: Cycling Chaos
type: journal_article
user_id: '15701'
year: '1995'
...
---
_id: '16288'
abstract:
- lang: eng
text: We derive a data-driven method for the approximation of the Koopman generator
called gEDMD, which can be regarded as a straightforward extension of EDMD (extended
dynamic mode decomposition). This approach is applicable to deterministic and
stochastic dynamical systems. It can be used for computing eigenvalues, eigenfunctions,
and modes of the generator and for system identification. In addition to learning
the governing equations of deterministic systems, which then reduces to SINDy
(sparse identification of nonlinear dynamics), it is possible to identify the
drift and diffusion terms of stochastic differential equations from data. Moreover,
we apply gEDMD to derive coarse-grained models of high-dimensional systems, and
also to determine efficient model predictive control strategies. We highlight
relationships with other methods and demonstrate the efficacy of the proposed
methods using several guiding examples and prototypical molecular dynamics problems.
article_number: '132416'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Jan-Hendrik
full_name: Niemann, Jan-Hendrik
last_name: Niemann
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
- first_name: Christof
full_name: Schütte, Christof
last_name: Schütte
citation:
ama: 'Klus S, Nüske F, Peitz S, Niemann J-H, Clementi C, Schütte C. Data-driven
approximation of the Koopman generator: Model reduction, system identification,
and control. Physica D: Nonlinear Phenomena. 2020;406. doi:10.1016/j.physd.2020.132416'
apa: 'Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., & Schütte,
C. (2020). Data-driven approximation of the Koopman generator: Model reduction,
system identification, and control. Physica D: Nonlinear Phenomena, 406.
https://doi.org/10.1016/j.physd.2020.132416'
bibtex: '@article{Klus_Nüske_Peitz_Niemann_Clementi_Schütte_2020, title={Data-driven
approximation of the Koopman generator: Model reduction, system identification,
and control}, volume={406}, DOI={10.1016/j.physd.2020.132416},
number={132416}, journal={Physica D: Nonlinear Phenomena}, author={Klus, Stefan
and Nüske, Feliks and Peitz, Sebastian and Niemann, Jan-Hendrik and Clementi,
Cecilia and Schütte, Christof}, year={2020} }'
chicago: 'Klus, Stefan, Feliks Nüske, Sebastian Peitz, Jan-Hendrik Niemann, Cecilia
Clementi, and Christof Schütte. “Data-Driven Approximation of the Koopman Generator:
Model Reduction, System Identification, and Control.” Physica D: Nonlinear
Phenomena 406 (2020). https://doi.org/10.1016/j.physd.2020.132416.'
ieee: 'S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, and C. Schütte,
“Data-driven approximation of the Koopman generator: Model reduction, system identification,
and control,” Physica D: Nonlinear Phenomena, vol. 406, 2020.'
mla: 'Klus, Stefan, et al. “Data-Driven Approximation of the Koopman Generator:
Model Reduction, System Identification, and Control.” Physica D: Nonlinear
Phenomena, vol. 406, 132416, 2020, doi:10.1016/j.physd.2020.132416.'
short: 'S. Klus, F. Nüske, S. Peitz, J.-H. Niemann, C. Clementi, C. Schütte, Physica
D: Nonlinear Phenomena 406 (2020).'
date_created: 2020-03-13T12:35:40Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1016/j.physd.2020.132416
intvolume: ' 406'
language:
- iso: eng
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
issn:
- 0167-2789
publication_status: published
status: public
title: 'Data-driven approximation of the Koopman generator: Model reduction, system
identification, and control'
type: journal_article
user_id: '47427'
volume: 406
year: '2020'
...
---
_id: '16309'
abstract:
- lang: eng
text: "In recent years, the success of the Koopman operator in dynamical systems\r\nanalysis
has also fueled the development of Koopman operator-based control\r\nframeworks.
In order to preserve the relatively low data requirements for an\r\napproximation
via Dynamic Mode Decomposition, a quantization approach was\r\nrecently proposed
in [Peitz & Klus, Automatica 106, 2019]. This way, control\r\nof nonlinear dynamical
systems can be realized by means of switched systems\r\ntechniques, using only
a finite set of autonomous Koopman operator-based\r\nreduced models. These individual
systems can be approximated very efficiently\r\nfrom data. The main idea is to
transform a control system into a set of\r\nautonomous systems for which the optimal
switching sequence has to be computed.\r\nIn this article, we extend these results
to continuous control inputs using\r\nrelaxation. This way, we combine the advantages
of the data efficiency of\r\napproximating a finite set of autonomous systems
with continuous controls. We\r\nshow that when using the Koopman generator, this
relaxation --- realized by\r\nlinear interpolation between two operators --- does
not introduce any error for\r\ncontrol affine systems. This allows us to control
high-dimensional nonlinear\r\nsystems using bilinear, low-dimensional surrogate
models. The efficiency of the\r\nproposed approach is demonstrated using several
examples with increasing\r\ncomplexity, from the Duffing oscillator to the chaotic
fluidic pinball."
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Samuel E.
full_name: Otto, Samuel E.
last_name: Otto
- first_name: Clarence W.
full_name: Rowley, Clarence W.
last_name: Rowley
citation:
ama: Peitz S, Otto SE, Rowley CW. Data-Driven Model Predictive Control using Interpolated
Koopman Generators. SIAM Journal on Applied Dynamical Systems. 2020;19(3):2162-2193.
doi:10.1137/20M1325678
apa: Peitz, S., Otto, S. E., & Rowley, C. W. (2020). Data-Driven Model Predictive
Control using Interpolated Koopman Generators. SIAM Journal on Applied Dynamical
Systems, 19(3), 2162–2193. https://doi.org/10.1137/20M1325678
bibtex: '@article{Peitz_Otto_Rowley_2020, title={Data-Driven Model Predictive Control
using Interpolated Koopman Generators}, volume={19}, DOI={10.1137/20M1325678},
number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Peitz,
Sebastian and Otto, Samuel E. and Rowley, Clarence W.}, year={2020}, pages={2162–2193}
}'
chicago: 'Peitz, Sebastian, Samuel E. Otto, and Clarence W. Rowley. “Data-Driven
Model Predictive Control Using Interpolated Koopman Generators.” SIAM Journal
on Applied Dynamical Systems 19, no. 3 (2020): 2162–93. https://doi.org/10.1137/20M1325678.'
ieee: S. Peitz, S. E. Otto, and C. W. Rowley, “Data-Driven Model Predictive Control
using Interpolated Koopman Generators,” SIAM Journal on Applied Dynamical
Systems, vol. 19, no. 3, pp. 2162–2193, 2020.
mla: Peitz, Sebastian, et al. “Data-Driven Model Predictive Control Using Interpolated
Koopman Generators.” SIAM Journal on Applied Dynamical Systems, vol. 19,
no. 3, 2020, pp. 2162–93, doi:10.1137/20M1325678.
short: S. Peitz, S.E. Otto, C.W. Rowley, SIAM Journal on Applied Dynamical Systems
19 (2020) 2162–2193.
date_created: 2020-03-17T09:53:01Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1137/20M1325678
intvolume: ' 19'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/pdf/10.1137/20M1325678
page: 2162-2193
publication: SIAM Journal on Applied Dynamical Systems
status: public
title: Data-Driven Model Predictive Control using Interpolated Koopman Generators
type: journal_article
user_id: '47427'
volume: 19
year: '2020'
...
---
_id: '21941'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
- first_name: Hao
full_name: Wu, Hao
last_name: Wu
- first_name: Ioannis
full_name: Kevrekidis, Ioannis
last_name: Kevrekidis
- first_name: Christof
full_name: Schütte, Christof
last_name: Schütte
- first_name: Frank
full_name: Noé, Frank
last_name: Noé
citation:
ama: Klus S, Nüske F, Koltai P, et al. Data-Driven Model Reduction and Transfer
Operator Approximation. Journal of Nonlinear Science. 2018:985-1010. doi:10.1007/s00332-017-9437-7
apa: Klus, S., Nüske, F., Koltai, P., Wu, H., Kevrekidis, I., Schütte, C., &
Noé, F. (2018). Data-Driven Model Reduction and Transfer Operator Approximation.
Journal of Nonlinear Science, 985–1010. https://doi.org/10.1007/s00332-017-9437-7
bibtex: '@article{Klus_Nüske_Koltai_Wu_Kevrekidis_Schütte_Noé_2018, title={Data-Driven
Model Reduction and Transfer Operator Approximation}, DOI={10.1007/s00332-017-9437-7},
journal={Journal of Nonlinear Science}, author={Klus, Stefan and Nüske, Feliks
and Koltai, Péter and Wu, Hao and Kevrekidis, Ioannis and Schütte, Christof and
Noé, Frank}, year={2018}, pages={985–1010} }'
chicago: Klus, Stefan, Feliks Nüske, Péter Koltai, Hao Wu, Ioannis Kevrekidis, Christof
Schütte, and Frank Noé. “Data-Driven Model Reduction and Transfer Operator Approximation.”
Journal of Nonlinear Science, 2018, 985–1010. https://doi.org/10.1007/s00332-017-9437-7.
ieee: S. Klus et al., “Data-Driven Model Reduction and Transfer Operator
Approximation,” Journal of Nonlinear Science, pp. 985–1010, 2018.
mla: Klus, Stefan, et al. “Data-Driven Model Reduction and Transfer Operator Approximation.”
Journal of Nonlinear Science, 2018, pp. 985–1010, doi:10.1007/s00332-017-9437-7.
short: S. Klus, F. Nüske, P. Koltai, H. Wu, I. Kevrekidis, C. Schütte, F. Noé, Journal
of Nonlinear Science (2018) 985–1010.
date_created: 2021-04-30T16:59:03Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1007/s00332-017-9437-7
extern: '1'
language:
- iso: eng
page: 985-1010
publication: Journal of Nonlinear Science
publication_identifier:
issn:
- 0938-8974
- 1432-1467
publication_status: published
status: public
title: Data-Driven Model Reduction and Transfer Operator Approximation
type: journal_article
user_id: '81513'
year: '2018'
...
---
_id: '16290'
abstract:
- lang: eng
text: The control of complex systems is of critical importance in many branches
of science, engineering, and industry, many of which are governed by nonlinear
partial differential equations. Controlling an unsteady fluid flow is particularly
important, as flow control is a key enabler for technologies in energy (e.g.,
wind, tidal, and combustion), transportation (e.g., planes, trains, and automobiles),
security (e.g., tracking airborne contamination), and health (e.g., artificial
hearts and artificial respiration). However, the high-dimensional, nonlinear,
and multi-scale dynamics make real-time feedback control infeasible. Fortunately,
these high- dimensional systems exhibit dominant, low-dimensional patterns of
activity that can be exploited for effective control in the sense that knowledge
of the entire state of a system is not required. Advances in machine learning
have the potential to revolutionize flow control given its ability to extract
principled, low-rank feature spaces characterizing such complex systems.We present
a novel deep learning modelpredictive control framework that exploits low-rank
features of the flow in order to achieve considerable improvements to control
performance. Instead of predicting the entire fluid state, we use a recurrent
neural network (RNN) to accurately predict the control relevant quantities of
the system, which are then embedded into an MPC framework to construct a feedback
loop. In order to lower the data requirements and to improve the prediction accuracy
and thus the control performance, incoming sensor data are used to update the
RNN online. The results are validated using varying fluid flow examples of increasing
complexity.
article_type: original
author:
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Steven L.
full_name: Brunton, Steven L.
last_name: Brunton
- first_name: J. Nathan
full_name: Kutz, J. Nathan
last_name: Kutz
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Bieker K, Peitz S, Brunton SL, Kutz JN, Dellnitz M. Deep model predictive flow
control with limited sensor data and online learning. Theoretical and Computational
Fluid Dynamics. 2020;34:577–591. doi:10.1007/s00162-020-00520-4
apa: Bieker, K., Peitz, S., Brunton, S. L., Kutz, J. N., & Dellnitz, M. (2020).
Deep model predictive flow control with limited sensor data and online learning.
Theoretical and Computational Fluid Dynamics, 34, 577–591. https://doi.org/10.1007/s00162-020-00520-4
bibtex: '@article{Bieker_Peitz_Brunton_Kutz_Dellnitz_2020, title={Deep model predictive
flow control with limited sensor data and online learning}, volume={34}, DOI={10.1007/s00162-020-00520-4},
journal={Theoretical and Computational Fluid Dynamics}, author={Bieker, Katharina
and Peitz, Sebastian and Brunton, Steven L. and Kutz, J. Nathan and Dellnitz,
Michael}, year={2020}, pages={577–591} }'
chicago: 'Bieker, Katharina, Sebastian Peitz, Steven L. Brunton, J. Nathan Kutz,
and Michael Dellnitz. “Deep Model Predictive Flow Control with Limited Sensor
Data and Online Learning.” Theoretical and Computational Fluid Dynamics
34 (2020): 577–591. https://doi.org/10.1007/s00162-020-00520-4.'
ieee: K. Bieker, S. Peitz, S. L. Brunton, J. N. Kutz, and M. Dellnitz, “Deep model
predictive flow control with limited sensor data and online learning,” Theoretical
and Computational Fluid Dynamics, vol. 34, pp. 577–591, 2020.
mla: Bieker, Katharina, et al. “Deep Model Predictive Flow Control with Limited
Sensor Data and Online Learning.” Theoretical and Computational Fluid Dynamics,
vol. 34, 2020, pp. 577–591, doi:10.1007/s00162-020-00520-4.
short: K. Bieker, S. Peitz, S.L. Brunton, J.N. Kutz, M. Dellnitz, Theoretical and
Computational Fluid Dynamics 34 (2020) 577–591.
date_created: 2020-03-13T12:40:09Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/s00162-020-00520-4
intvolume: ' 34'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s00162-020-00520-4.pdf
oa: '1'
page: 577–591
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Theoretical and Computational Fluid Dynamics
publication_identifier:
issn:
- 0935-4964
- 1432-2250
publication_status: published
status: public
title: Deep model predictive flow control with limited sensor data and online learning
type: journal_article
user_id: '47427'
volume: 34
year: '2020'
...
---
_id: '21337'
abstract:
- lang: eng
text: "We present a flexible trust region descend algorithm for unconstrained and\r\nconvexly
constrained multiobjective optimization problems. It is targeted at\r\nheterogeneous
and expensive problems, i.e., problems that have at least one\r\nobjective function
that is computationally expensive. The method is\r\nderivative-free in the sense
that neither need derivative information be\r\navailable for the expensive objectives
nor are gradients approximated using\r\nrepeated function evaluations as is the
case in finite-difference methods.\r\nInstead, a multiobjective trust region approach
is used that works similarly to\r\nits well-known scalar pendants. Local surrogate
models constructed from\r\nevaluation data of the true objective functions are
employed to compute\r\npossible descent directions. In contrast to existing multiobjective
trust\r\nregion algorithms, these surrogates are not polynomial but carefully\r\nconstructed
radial basis function networks. This has the important advantage\r\nthat the number
of data points scales linearly with the parameter space\r\ndimension. The local
models qualify as fully linear and the corresponding\r\ngeneral scalar framework
is adapted for problems with multiple objectives.\r\nConvergence to Pareto critical
points is proven and numerical examples\r\nillustrate our findings."
article_number: '31'
author:
- first_name: Manuel Bastian
full_name: Berkemeier, Manuel Bastian
id: '51701'
last_name: Berkemeier
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Berkemeier MB, Peitz S. Derivative-Free Multiobjective Trust Region Descent
Method Using Radial Basis Function Surrogate Models. Mathematical and Computational
Applications. 2021;26(2). doi:10.3390/mca26020031
apa: Berkemeier, M. B., & Peitz, S. (2021). Derivative-Free Multiobjective Trust
Region Descent Method Using Radial Basis Function Surrogate Models. Mathematical
and Computational Applications, 26(2). https://doi.org/10.3390/mca26020031
bibtex: '@article{Berkemeier_Peitz_2021, title={Derivative-Free Multiobjective Trust
Region Descent Method Using Radial Basis Function Surrogate Models}, volume={26},
DOI={10.3390/mca26020031}, number={231},
journal={Mathematical and Computational Applications}, author={Berkemeier, Manuel
Bastian and Peitz, Sebastian}, year={2021} }'
chicago: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective
Trust Region Descent Method Using Radial Basis Function Surrogate Models.” Mathematical
and Computational Applications 26, no. 2 (2021). https://doi.org/10.3390/mca26020031.
ieee: M. B. Berkemeier and S. Peitz, “Derivative-Free Multiobjective Trust Region
Descent Method Using Radial Basis Function Surrogate Models,” Mathematical
and Computational Applications, vol. 26, no. 2, 2021.
mla: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Derivative-Free Multiobjective
Trust Region Descent Method Using Radial Basis Function Surrogate Models.” Mathematical
and Computational Applications, vol. 26, no. 2, 31, 2021, doi:10.3390/mca26020031.
short: M.B. Berkemeier, S. Peitz, Mathematical and Computational Applications 26
(2021).
date_created: 2021-03-01T10:46:48Z
date_updated: 2022-01-06T06:54:55Z
department:
- _id: '101'
- _id: '655'
doi: 10.3390/mca26020031
intvolume: ' 26'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/2297-8747/26/2/31/pdf
oa: '1'
publication: Mathematical and Computational Applications
publication_identifier:
eissn:
- 2297-8747
publication_status: published
status: public
title: Derivative-Free Multiobjective Trust Region Descent Method Using Radial Basis
Function Surrogate Models
type: journal_article
user_id: '47427'
volume: 26
year: '2021'
...
---
_id: '16631'
author:
- first_name: R.
full_name: Li, R.
last_name: Li
- first_name: A.
full_name: Pottharst, A.
last_name: Pottharst
- first_name: N.
full_name: Frohieke, N.
last_name: Frohieke
- first_name: J.
full_name: Becker, J.
last_name: Becker
- first_name: K.
full_name: Witting, K.
last_name: Witting
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
- first_name: O.
full_name: Znamenshchykov, O.
last_name: Znamenshchykov
- first_name: R.
full_name: Feldmann, R.
last_name: Feldmann
citation:
ama: 'Li R, Pottharst A, Frohieke N, et al. Design and implementation of a hybrid
energy supply system for railway vehicles. In: Twentieth Annual IEEE Applied
Power Electronics Conference and Exposition, 2005. APEC 2005. ; 2005. doi:10.1109/apec.2005.1452979'
apa: Li, R., Pottharst, A., Frohieke, N., Becker, J., Witting, K., Dellnitz, M.,
… Feldmann, R. (2005). Design and implementation of a hybrid energy supply system
for railway vehicles. In Twentieth Annual IEEE Applied Power Electronics Conference
and Exposition, 2005. APEC 2005. https://doi.org/10.1109/apec.2005.1452979
bibtex: '@inproceedings{Li_Pottharst_Frohieke_Becker_Witting_Dellnitz_Znamenshchykov_Feldmann_2005,
title={Design and implementation of a hybrid energy supply system for railway
vehicles}, DOI={10.1109/apec.2005.1452979},
booktitle={Twentieth Annual IEEE Applied Power Electronics Conference and Exposition,
2005. APEC 2005.}, author={Li, R. and Pottharst, A. and Frohieke, N. and Becker,
J. and Witting, K. and Dellnitz, M. and Znamenshchykov, O. and Feldmann, R.},
year={2005} }'
chicago: Li, R., A. Pottharst, N. Frohieke, J. Becker, K. Witting, M. Dellnitz,
O. Znamenshchykov, and R. Feldmann. “Design and Implementation of a Hybrid Energy
Supply System for Railway Vehicles.” In Twentieth Annual IEEE Applied Power
Electronics Conference and Exposition, 2005. APEC 2005., 2005. https://doi.org/10.1109/apec.2005.1452979.
ieee: R. Li et al., “Design and implementation of a hybrid energy supply
system for railway vehicles,” in Twentieth Annual IEEE Applied Power Electronics
Conference and Exposition, 2005. APEC 2005., 2005.
mla: Li, R., et al. “Design and Implementation of a Hybrid Energy Supply System
for Railway Vehicles.” Twentieth Annual IEEE Applied Power Electronics Conference
and Exposition, 2005. APEC 2005., 2005, doi:10.1109/apec.2005.1452979.
short: 'R. Li, A. Pottharst, N. Frohieke, J. Becker, K. Witting, M. Dellnitz, O.
Znamenshchykov, R. Feldmann, in: Twentieth Annual IEEE Applied Power Electronics
Conference and Exposition, 2005. APEC 2005., 2005.'
date_created: 2020-04-16T08:29:47Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1109/apec.2005.1452979
publication: Twentieth Annual IEEE Applied Power Electronics Conference and Exposition,
2005. APEC 2005.
publication_identifier:
isbn:
- '0780389751'
publication_status: published
status: public
title: Design and implementation of a hybrid energy supply system for railway vehicles
type: conference
user_id: '15701'
year: '2005'
...
---
_id: '16669'
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Massimiliano
full_name: Vasile, Massimiliano
last_name: Vasile
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Dario
full_name: Izzo, Dario
last_name: Izzo
citation:
ama: Schütze O, Vasile M, Junge O, Dellnitz M, Izzo D. Designing optimal low-thrust
gravity-assist trajectories using space pruning and a multi-objective approach.
Engineering Optimization. 2009:155-181. doi:10.1080/03052150802391734
apa: Schütze, O., Vasile, M., Junge, O., Dellnitz, M., & Izzo, D. (2009). Designing
optimal low-thrust gravity-assist trajectories using space pruning and a multi-objective
approach. Engineering Optimization, 155–181. https://doi.org/10.1080/03052150802391734
bibtex: '@article{Schütze_Vasile_Junge_Dellnitz_Izzo_2009, title={Designing optimal
low-thrust gravity-assist trajectories using space pruning and a multi-objective
approach}, DOI={10.1080/03052150802391734},
journal={Engineering Optimization}, author={Schütze, Oliver and Vasile, Massimiliano
and Junge, Oliver and Dellnitz, Michael and Izzo, Dario}, year={2009}, pages={155–181}
}'
chicago: Schütze, Oliver, Massimiliano Vasile, Oliver Junge, Michael Dellnitz, and
Dario Izzo. “Designing Optimal Low-Thrust Gravity-Assist Trajectories Using Space
Pruning and a Multi-Objective Approach.” Engineering Optimization, 2009,
155–81. https://doi.org/10.1080/03052150802391734.
ieee: O. Schütze, M. Vasile, O. Junge, M. Dellnitz, and D. Izzo, “Designing optimal
low-thrust gravity-assist trajectories using space pruning and a multi-objective
approach,” Engineering Optimization, pp. 155–181, 2009.
mla: Schütze, Oliver, et al. “Designing Optimal Low-Thrust Gravity-Assist Trajectories
Using Space Pruning and a Multi-Objective Approach.” Engineering Optimization,
2009, pp. 155–81, doi:10.1080/03052150802391734.
short: O. Schütze, M. Vasile, O. Junge, M. Dellnitz, D. Izzo, Engineering Optimization
(2009) 155–181.
date_created: 2020-04-16T10:04:50Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1080/03052150802391734
language:
- iso: eng
page: 155-181
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: Designing optimal low-thrust gravity-assist trajectories using space pruning
and a multi-objective approach
type: journal_article
user_id: '15701'
year: '2009'
...
---
_id: '16600'
author:
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Froyland G, Dellnitz M. Detecting and Locating Near-Optimal Almost-Invariant
Sets and Cycles. SIAM Journal on Scientific Computing. 2003:1839-1863.
doi:10.1137/s106482750238911x
apa: Froyland, G., & Dellnitz, M. (2003). Detecting and Locating Near-Optimal
Almost-Invariant Sets and Cycles. SIAM Journal on Scientific Computing,
1839–1863. https://doi.org/10.1137/s106482750238911x
bibtex: '@article{Froyland_Dellnitz_2003, title={Detecting and Locating Near-Optimal
Almost-Invariant Sets and Cycles}, DOI={10.1137/s106482750238911x},
journal={SIAM Journal on Scientific Computing}, author={Froyland, Gary and Dellnitz,
Michael}, year={2003}, pages={1839–1863} }'
chicago: Froyland, Gary, and Michael Dellnitz. “Detecting and Locating Near-Optimal
Almost-Invariant Sets and Cycles.” SIAM Journal on Scientific Computing,
2003, 1839–63. https://doi.org/10.1137/s106482750238911x.
ieee: G. Froyland and M. Dellnitz, “Detecting and Locating Near-Optimal Almost-Invariant
Sets and Cycles,” SIAM Journal on Scientific Computing, pp. 1839–1863,
2003.
mla: Froyland, Gary, and Michael Dellnitz. “Detecting and Locating Near-Optimal
Almost-Invariant Sets and Cycles.” SIAM Journal on Scientific Computing,
2003, pp. 1839–63, doi:10.1137/s106482750238911x.
short: G. Froyland, M. Dellnitz, SIAM Journal on Scientific Computing (2003) 1839–1863.
date_created: 2020-04-16T06:07:10Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1137/s106482750238911x
language:
- iso: eng
page: 1839-1863
publication: SIAM Journal on Scientific Computing
publication_identifier:
issn:
- 1064-8275
- 1095-7197
publication_status: published
status: public
title: Detecting and Locating Near-Optimal Almost-Invariant Sets and Cycles
type: journal_article
user_id: '15701'
year: '2003'
...
---
_id: '16675'
author:
- first_name: Bianca
full_name: Thiere, Bianca
last_name: Thiere
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Pierpaolo
full_name: Pergola, Pierpaolo
last_name: Pergola
citation:
ama: 'Thiere B, Ober-Blöbaum S, Pergola P. Detecting Initial Guesses for Trajectories
in the (P)CRTBP. In: AIAA/AAS Astrodynamics Specialist Conference. ; 2010.
doi:10.2514/6.2010-7962'
apa: Thiere, B., Ober-Blöbaum, S., & Pergola, P. (2010). Detecting Initial Guesses
for Trajectories in the (P)CRTBP. In AIAA/AAS Astrodynamics Specialist Conference.
https://doi.org/10.2514/6.2010-7962
bibtex: '@inproceedings{Thiere_Ober-Blöbaum_Pergola_2010, title={Detecting Initial
Guesses for Trajectories in the (P)CRTBP}, DOI={10.2514/6.2010-7962},
booktitle={AIAA/AAS Astrodynamics Specialist Conference}, author={Thiere, Bianca
and Ober-Blöbaum, Sina and Pergola, Pierpaolo}, year={2010} }'
chicago: Thiere, Bianca, Sina Ober-Blöbaum, and Pierpaolo Pergola. “Detecting Initial
Guesses for Trajectories in the (P)CRTBP.” In AIAA/AAS Astrodynamics Specialist
Conference, 2010. https://doi.org/10.2514/6.2010-7962.
ieee: B. Thiere, S. Ober-Blöbaum, and P. Pergola, “Detecting Initial Guesses for
Trajectories in the (P)CRTBP,” in AIAA/AAS Astrodynamics Specialist Conference,
2010.
mla: Thiere, Bianca, et al. “Detecting Initial Guesses for Trajectories in the (P)CRTBP.”
AIAA/AAS Astrodynamics Specialist Conference, 2010, doi:10.2514/6.2010-7962.
short: 'B. Thiere, S. Ober-Blöbaum, P. Pergola, in: AIAA/AAS Astrodynamics Specialist
Conference, 2010.'
date_created: 2020-04-16T10:11:57Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.2514/6.2010-7962
language:
- iso: eng
publication: AIAA/AAS Astrodynamics Specialist Conference
publication_identifier:
isbn:
- '9781624101502'
publication_status: published
status: public
title: Detecting Initial Guesses for Trajectories in the (P)CRTBP
type: conference
user_id: '15701'
year: '2010'
...
---
_id: '16518'
author:
- first_name: Ernest
full_name: Barany, Ernest
last_name: Barany
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Martin
full_name: Golubitsky, Martin
last_name: Golubitsky
citation:
ama: 'Barany E, Dellnitz M, Golubitsky M. Detecting the symmetry of attractors.
Physica D: Nonlinear Phenomena. 1993:66-87. doi:10.1016/0167-2789(93)90198-a'
apa: 'Barany, E., Dellnitz, M., & Golubitsky, M. (1993). Detecting the symmetry
of attractors. Physica D: Nonlinear Phenomena, 66–87. https://doi.org/10.1016/0167-2789(93)90198-a'
bibtex: '@article{Barany_Dellnitz_Golubitsky_1993, title={Detecting the symmetry
of attractors}, DOI={10.1016/0167-2789(93)90198-a},
journal={Physica D: Nonlinear Phenomena}, author={Barany, Ernest and Dellnitz,
Michael and Golubitsky, Martin}, year={1993}, pages={66–87} }'
chicago: 'Barany, Ernest, Michael Dellnitz, and Martin Golubitsky. “Detecting the
Symmetry of Attractors.” Physica D: Nonlinear Phenomena, 1993, 66–87. https://doi.org/10.1016/0167-2789(93)90198-a.'
ieee: 'E. Barany, M. Dellnitz, and M. Golubitsky, “Detecting the symmetry of attractors,”
Physica D: Nonlinear Phenomena, pp. 66–87, 1993.'
mla: 'Barany, Ernest, et al. “Detecting the Symmetry of Attractors.” Physica
D: Nonlinear Phenomena, 1993, pp. 66–87, doi:10.1016/0167-2789(93)90198-a.'
short: 'E. Barany, M. Dellnitz, M. Golubitsky, Physica D: Nonlinear Phenomena (1993)
66–87.'
date_created: 2020-04-15T08:02:09Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1016/0167-2789(93)90198-a
language:
- iso: eng
page: 66-87
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
issn:
- 0167-2789
publication_status: published
status: public
title: Detecting the symmetry of attractors
type: journal_article
user_id: '15701'
year: '1993'
...
---
_id: '16602'
author:
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Kathrin
full_name: Padberg, Kathrin
last_name: Padberg
- first_name: Matthew H.
full_name: England, Matthew H.
last_name: England
- first_name: Anne Marie
full_name: Treguier, Anne Marie
last_name: Treguier
citation:
ama: Froyland G, Padberg K, England MH, Treguier AM. Detection of Coherent Oceanic
Structures via Transfer Operators. Physical Review Letters. 2007. doi:10.1103/physrevlett.98.224503
apa: Froyland, G., Padberg, K., England, M. H., & Treguier, A. M. (2007). Detection
of Coherent Oceanic Structures via Transfer Operators. Physical Review Letters.
https://doi.org/10.1103/physrevlett.98.224503
bibtex: '@article{Froyland_Padberg_England_Treguier_2007, title={Detection of Coherent
Oceanic Structures via Transfer Operators}, DOI={10.1103/physrevlett.98.224503},
journal={Physical Review Letters}, author={Froyland, Gary and Padberg, Kathrin
and England, Matthew H. and Treguier, Anne Marie}, year={2007} }'
chicago: Froyland, Gary, Kathrin Padberg, Matthew H. England, and Anne Marie Treguier.
“Detection of Coherent Oceanic Structures via Transfer Operators.” Physical
Review Letters, 2007. https://doi.org/10.1103/physrevlett.98.224503.
ieee: G. Froyland, K. Padberg, M. H. England, and A. M. Treguier, “Detection of
Coherent Oceanic Structures via Transfer Operators,” Physical Review Letters,
2007.
mla: Froyland, Gary, et al. “Detection of Coherent Oceanic Structures via Transfer
Operators.” Physical Review Letters, 2007, doi:10.1103/physrevlett.98.224503.
short: G. Froyland, K. Padberg, M.H. England, A.M. Treguier, Physical Review Letters
(2007).
date_created: 2020-04-16T06:09:07Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1103/physrevlett.98.224503
language:
- iso: eng
publication: Physical Review Letters
publication_identifier:
issn:
- 0031-9007
- 1079-7114
publication_status: published
status: public
title: Detection of Coherent Oceanic Structures via Transfer Operators
type: journal_article
user_id: '15701'
year: '2007'
...
---
_id: '16586'
author:
- first_name: Robert
full_name: Elsässer, Robert
last_name: Elsässer
- first_name: Burkhard
full_name: Monien, Burkhard
last_name: Monien
- first_name: Robert
full_name: Preis, Robert
last_name: Preis
citation:
ama: Elsässer R, Monien B, Preis R. Diffusion Schemes for Load Balancing on Heterogeneous
Networks. Theory of Computing Systems. 2002:305-320. doi:10.1007/s00224-002-1056-4
apa: Elsässer, R., Monien, B., & Preis, R. (2002). Diffusion Schemes for Load
Balancing on Heterogeneous Networks. Theory of Computing Systems, 305–320.
https://doi.org/10.1007/s00224-002-1056-4
bibtex: '@article{Elsässer_Monien_Preis_2002, title={Diffusion Schemes for Load
Balancing on Heterogeneous Networks}, DOI={10.1007/s00224-002-1056-4},
journal={Theory of Computing Systems}, author={Elsässer, Robert and Monien, Burkhard
and Preis, Robert}, year={2002}, pages={305–320} }'
chicago: Elsässer, Robert, Burkhard Monien, and Robert Preis. “Diffusion Schemes
for Load Balancing on Heterogeneous Networks.” Theory of Computing Systems,
2002, 305–20. https://doi.org/10.1007/s00224-002-1056-4.
ieee: R. Elsässer, B. Monien, and R. Preis, “Diffusion Schemes for Load Balancing
on Heterogeneous Networks,” Theory of Computing Systems, pp. 305–320, 2002.
mla: Elsässer, Robert, et al. “Diffusion Schemes for Load Balancing on Heterogeneous
Networks.” Theory of Computing Systems, 2002, pp. 305–20, doi:10.1007/s00224-002-1056-4.
short: R. Elsässer, B. Monien, R. Preis, Theory of Computing Systems (2002) 305–320.
date_created: 2020-04-16T05:45:42Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/s00224-002-1056-4
language:
- iso: eng
page: 305-320
publication: Theory of Computing Systems
publication_identifier:
issn:
- 1432-4350
- 1433-0490
publication_status: published
status: public
title: Diffusion Schemes for Load Balancing on Heterogeneous Networks
type: journal_article
user_id: '15701'
year: '2002'
...
---
_id: '16635'
author:
- first_name: A.
full_name: Meyer, A.
last_name: Meyer
citation:
ama: Meyer A. Discontinuity Induced Bifurcations in Timed Continuous Petri Nets.
IFAC Proceedings Volumes. 2012:28-33. doi:10.3182/20121003-3-mx-4033.00008
apa: Meyer, A. (2012). Discontinuity Induced Bifurcations in Timed Continuous Petri
Nets. IFAC Proceedings Volumes, 28–33. https://doi.org/10.3182/20121003-3-mx-4033.00008
bibtex: '@article{Meyer_2012, title={Discontinuity Induced Bifurcations in Timed
Continuous Petri Nets}, DOI={10.3182/20121003-3-mx-4033.00008},
journal={IFAC Proceedings Volumes}, author={Meyer, A.}, year={2012}, pages={28–33}
}'
chicago: Meyer, A. “Discontinuity Induced Bifurcations in Timed Continuous Petri
Nets.” IFAC Proceedings Volumes, 2012, 28–33. https://doi.org/10.3182/20121003-3-mx-4033.00008.
ieee: A. Meyer, “Discontinuity Induced Bifurcations in Timed Continuous Petri Nets,”
IFAC Proceedings Volumes, pp. 28–33, 2012.
mla: Meyer, A. “Discontinuity Induced Bifurcations in Timed Continuous Petri Nets.”
IFAC Proceedings Volumes, 2012, pp. 28–33, doi:10.3182/20121003-3-mx-4033.00008.
short: A. Meyer, IFAC Proceedings Volumes (2012) 28–33.
date_created: 2020-04-16T08:33:42Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.3182/20121003-3-mx-4033.00008
language:
- iso: eng
page: 28-33
publication: IFAC Proceedings Volumes
publication_identifier:
issn:
- 1474-6670
publication_status: published
status: public
title: Discontinuity Induced Bifurcations in Timed Continuous Petri Nets
type: journal_article
user_id: '15701'
year: '2012'
...
---
_id: '16630'
abstract:
- lang: eng
text: This paper formulates the dynamical equations of mechanics subject
to holonomic constraints in terms of the states and controls using a constrained
version of the Lagrange-d’Alembert principle. Based on a discrete version of this
principle, a structure preserving time-stepping scheme is derived. It is shown
that this respect for the mechanical structure (such as a reliable computation
of the energy and momentum budget, without numerical dissipation) is retained
when the system is reduced to its minimal dimension by the discrete null space
method. Together with initial and final conditions on the configuration and conjugate
momentum, the reduced time-stepping equations serve as nonlinear equality constraints
for the minimisation of a given cost functional. The algorithm yields a sequence
of discrete configurations together with a sequence of actuating forces, optimally
guiding the system from the initial to the desired final state. The resulting
discrete optimal control algorithm is shown to have excellent energy and momentum
properties, which are illustrated by two specific examples, namely reorientation
and repositioning of a rigid body subject to external forces and the reorientation
of a rigid body with internal momentum wheels.
author:
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Jerrold E.
full_name: Marsden, Jerrold E.
last_name: Marsden
- first_name: Michael
full_name: Ortiz, Michael
last_name: Ortiz
citation:
ama: 'Leyendecker S, Ober-Blöbaum S, Marsden JE, Ortiz M. Discrete Mechanics and
Optimal Control for Constrained Multibody Dynamics. In: Volume 5: 6th International
Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B,
and C. ; 2007. doi:10.1115/detc2007-34574'
apa: 'Leyendecker, S., Ober-Blöbaum, S., Marsden, J. E., & Ortiz, M. (2007).
Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics. In
Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics,
and Control, Parts A, B, and C. https://doi.org/10.1115/detc2007-34574'
bibtex: '@inproceedings{Leyendecker_Ober-Blöbaum_Marsden_Ortiz_2007, title={Discrete
Mechanics and Optimal Control for Constrained Multibody Dynamics}, DOI={10.1115/detc2007-34574},
booktitle={Volume 5: 6th International Conference on Multibody Systems, Nonlinear
Dynamics, and Control, Parts A, B, and C}, author={Leyendecker, Sigrid and Ober-Blöbaum,
Sina and Marsden, Jerrold E. and Ortiz, Michael}, year={2007} }'
chicago: 'Leyendecker, Sigrid, Sina Ober-Blöbaum, Jerrold E. Marsden, and Michael
Ortiz. “Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics.”
In Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics,
and Control, Parts A, B, and C, 2007. https://doi.org/10.1115/detc2007-34574.'
ieee: 'S. Leyendecker, S. Ober-Blöbaum, J. E. Marsden, and M. Ortiz, “Discrete Mechanics
and Optimal Control for Constrained Multibody Dynamics,” in Volume 5: 6th International
Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B,
and C, 2007.'
mla: 'Leyendecker, Sigrid, et al. “Discrete Mechanics and Optimal Control for Constrained
Multibody Dynamics.” Volume 5: 6th International Conference on Multibody Systems,
Nonlinear Dynamics, and Control, Parts A, B, and C, 2007, doi:10.1115/detc2007-34574.'
short: 'S. Leyendecker, S. Ober-Blöbaum, J.E. Marsden, M. Ortiz, in: Volume 5: 6th
International Conference on Multibody Systems, Nonlinear Dynamics, and Control,
Parts A, B, and C, 2007.'
date_created: 2020-04-16T08:28:13Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1115/detc2007-34574
language:
- iso: eng
publication: 'Volume 5: 6th International Conference on Multibody Systems, Nonlinear
Dynamics, and Control, Parts A, B, and C'
publication_identifier:
isbn:
- 079184806X
publication_status: published
status: public
title: Discrete Mechanics and Optimal Control for Constrained Multibody Dynamics
type: conference
user_id: '15701'
year: '2007'
...
---
_id: '16582'
author:
- first_name: F.
full_name: Demoures, F.
last_name: Demoures
- first_name: F.
full_name: Gay-Balmaz, F.
last_name: Gay-Balmaz
- first_name: S.
full_name: Leyendecker, S.
last_name: Leyendecker
- first_name: S.
full_name: Ober-Blöbaum, S.
last_name: Ober-Blöbaum
- first_name: T. S.
full_name: Ratiu, T. S.
last_name: Ratiu
- first_name: Y.
full_name: Weinand, Y.
last_name: Weinand
citation:
ama: Demoures F, Gay-Balmaz F, Leyendecker S, Ober-Blöbaum S, Ratiu TS, Weinand
Y. Discrete variational Lie group formulation of geometrically exact beam dynamics.
Numerische Mathematik. 2015:73-123. doi:10.1007/s00211-014-0659-4
apa: Demoures, F., Gay-Balmaz, F., Leyendecker, S., Ober-Blöbaum, S., Ratiu, T.
S., & Weinand, Y. (2015). Discrete variational Lie group formulation of geometrically
exact beam dynamics. Numerische Mathematik, 73–123. https://doi.org/10.1007/s00211-014-0659-4
bibtex: '@article{Demoures_Gay-Balmaz_Leyendecker_Ober-Blöbaum_Ratiu_Weinand_2015,
title={Discrete variational Lie group formulation of geometrically exact beam
dynamics}, DOI={10.1007/s00211-014-0659-4},
journal={Numerische Mathematik}, author={Demoures, F. and Gay-Balmaz, F. and Leyendecker,
S. and Ober-Blöbaum, S. and Ratiu, T. S. and Weinand, Y.}, year={2015}, pages={73–123}
}'
chicago: Demoures, F., F. Gay-Balmaz, S. Leyendecker, S. Ober-Blöbaum, T. S. Ratiu,
and Y. Weinand. “Discrete Variational Lie Group Formulation of Geometrically Exact
Beam Dynamics.” Numerische Mathematik, 2015, 73–123. https://doi.org/10.1007/s00211-014-0659-4.
ieee: F. Demoures, F. Gay-Balmaz, S. Leyendecker, S. Ober-Blöbaum, T. S. Ratiu,
and Y. Weinand, “Discrete variational Lie group formulation of geometrically exact
beam dynamics,” Numerische Mathematik, pp. 73–123, 2015.
mla: Demoures, F., et al. “Discrete Variational Lie Group Formulation of Geometrically
Exact Beam Dynamics.” Numerische Mathematik, 2015, pp. 73–123, doi:10.1007/s00211-014-0659-4.
short: F. Demoures, F. Gay-Balmaz, S. Leyendecker, S. Ober-Blöbaum, T.S. Ratiu,
Y. Weinand, Numerische Mathematik (2015) 73–123.
date_created: 2020-04-16T05:40:13Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/s00211-014-0659-4
language:
- iso: eng
page: 73-123
publication: Numerische Mathematik
publication_identifier:
issn:
- 0029-599X
- 0945-3245
publication_status: published
status: public
title: Discrete variational Lie group formulation of geometrically exact beam dynamics
type: journal_article
user_id: '15701'
year: '2015'
...
---
_id: '16672'
author:
- first_name: Andreas
full_name: Specht, Andreas
last_name: Specht
- first_name: Sina
full_name: Ober-Blobaum, Sina
last_name: Ober-Blobaum
- first_name: Oliver
full_name: Wallscheid, Oliver
last_name: Wallscheid
- first_name: Christoph
full_name: Romaus, Christoph
last_name: Romaus
- first_name: Joachim
full_name: Bocker, Joachim
last_name: Bocker
citation:
ama: 'Specht A, Ober-Blobaum S, Wallscheid O, Romaus C, Bocker J. Discrete-time
model of an IPMSM based on variational integrators. In: 2013 International
Electric Machines & Drives Conference. ; 2013. doi:10.1109/iemdc.2013.6556322'
apa: Specht, A., Ober-Blobaum, S., Wallscheid, O., Romaus, C., & Bocker, J.
(2013). Discrete-time model of an IPMSM based on variational integrators. In 2013
International Electric Machines & Drives Conference. https://doi.org/10.1109/iemdc.2013.6556322
bibtex: '@inproceedings{Specht_Ober-Blobaum_Wallscheid_Romaus_Bocker_2013, title={Discrete-time
model of an IPMSM based on variational integrators}, DOI={10.1109/iemdc.2013.6556322},
booktitle={2013 International Electric Machines & Drives Conference}, author={Specht,
Andreas and Ober-Blobaum, Sina and Wallscheid, Oliver and Romaus, Christoph and
Bocker, Joachim}, year={2013} }'
chicago: Specht, Andreas, Sina Ober-Blobaum, Oliver Wallscheid, Christoph Romaus,
and Joachim Bocker. “Discrete-Time Model of an IPMSM Based on Variational Integrators.”
In 2013 International Electric Machines & Drives Conference, 2013.
https://doi.org/10.1109/iemdc.2013.6556322.
ieee: A. Specht, S. Ober-Blobaum, O. Wallscheid, C. Romaus, and J. Bocker, “Discrete-time
model of an IPMSM based on variational integrators,” in 2013 International
Electric Machines & Drives Conference, 2013.
mla: Specht, Andreas, et al. “Discrete-Time Model of an IPMSM Based on Variational
Integrators.” 2013 International Electric Machines & Drives Conference,
2013, doi:10.1109/iemdc.2013.6556322.
short: 'A. Specht, S. Ober-Blobaum, O. Wallscheid, C. Romaus, J. Bocker, in: 2013
International Electric Machines & Drives Conference, 2013.'
date_created: 2020-04-16T10:09:01Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1109/iemdc.2013.6556322
publication: 2013 International Electric Machines & Drives Conference
publication_identifier:
isbn:
- '9781467349741'
- '9781467349758'
- '9781467349727'
- '9781467349734'
publication_status: published
status: public
title: Discrete-time model of an IPMSM based on variational integrators
type: conference
user_id: '15701'
year: '2013'
...
---
_id: '16594'
author:
- first_name: Kathrin
full_name: Flasskamp, Kathrin
last_name: Flasskamp
- first_name: Todd
full_name: Murphey, Todd
last_name: Murphey
- first_name: Sina
full_name: Ober-Blobaum, Sina
last_name: Ober-Blobaum
citation:
ama: 'Flasskamp K, Murphey T, Ober-Blobaum S. Discretized switching time optimization
problems. In: 2013 European Control Conference (ECC). ; 2013. doi:10.23919/ecc.2013.6669577'
apa: Flasskamp, K., Murphey, T., & Ober-Blobaum, S. (2013). Discretized switching
time optimization problems. In 2013 European Control Conference (ECC).
https://doi.org/10.23919/ecc.2013.6669577
bibtex: '@inproceedings{Flasskamp_Murphey_Ober-Blobaum_2013, title={Discretized
switching time optimization problems}, DOI={10.23919/ecc.2013.6669577},
booktitle={2013 European Control Conference (ECC)}, author={Flasskamp, Kathrin
and Murphey, Todd and Ober-Blobaum, Sina}, year={2013} }'
chicago: Flasskamp, Kathrin, Todd Murphey, and Sina Ober-Blobaum. “Discretized Switching
Time Optimization Problems.” In 2013 European Control Conference (ECC),
2013. https://doi.org/10.23919/ecc.2013.6669577.
ieee: K. Flasskamp, T. Murphey, and S. Ober-Blobaum, “Discretized switching time
optimization problems,” in 2013 European Control Conference (ECC), 2013.
mla: Flasskamp, Kathrin, et al. “Discretized Switching Time Optimization Problems.”
2013 European Control Conference (ECC), 2013, doi:10.23919/ecc.2013.6669577.
short: 'K. Flasskamp, T. Murphey, S. Ober-Blobaum, in: 2013 European Control Conference
(ECC), 2013.'
date_created: 2020-04-16T05:56:11Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.23919/ecc.2013.6669577
language:
- iso: eng
publication: 2013 European Control Conference (ECC)
publication_identifier:
isbn:
- '9783033039629'
publication_status: published
status: public
title: Discretized switching time optimization problems
type: conference
user_id: '15701'
year: '2013'
...
---
_id: '16623'
author:
- first_name: Benjamin
full_name: Klöpper, Benjamin
last_name: Klöpper
- first_name: Herbert
full_name: Podlogar, Herbert
last_name: Podlogar
- first_name: Jürgen
full_name: Gausemeier, Jürgen
last_name: Gausemeier
- first_name: Katrin
full_name: Witting, Katrin
last_name: Witting
citation:
ama: 'Klöpper B, Podlogar H, Gausemeier J, Witting K. Domain Spanning Search for
the Identification of Solution Patterns for the Conceptual Design of Self-Optimizing
Systems. In: 2008 19th International Conference on Database and Expert Systems
Applications. ; 2008. doi:10.1109/dexa.2008.111'
apa: Klöpper, B., Podlogar, H., Gausemeier, J., & Witting, K. (2008). Domain
Spanning Search for the Identification of Solution Patterns for the Conceptual
Design of Self-Optimizing Systems. In 2008 19th International Conference on
Database and Expert Systems Applications. https://doi.org/10.1109/dexa.2008.111
bibtex: '@inproceedings{Klöpper_Podlogar_Gausemeier_Witting_2008, title={Domain
Spanning Search for the Identification of Solution Patterns for the Conceptual
Design of Self-Optimizing Systems}, DOI={10.1109/dexa.2008.111},
booktitle={2008 19th International Conference on Database and Expert Systems Applications},
author={Klöpper, Benjamin and Podlogar, Herbert and Gausemeier, Jürgen and Witting,
Katrin}, year={2008} }'
chicago: Klöpper, Benjamin, Herbert Podlogar, Jürgen Gausemeier, and Katrin Witting.
“Domain Spanning Search for the Identification of Solution Patterns for the Conceptual
Design of Self-Optimizing Systems.” In 2008 19th International Conference on
Database and Expert Systems Applications, 2008. https://doi.org/10.1109/dexa.2008.111.
ieee: B. Klöpper, H. Podlogar, J. Gausemeier, and K. Witting, “Domain Spanning Search
for the Identification of Solution Patterns for the Conceptual Design of Self-Optimizing
Systems,” in 2008 19th International Conference on Database and Expert Systems
Applications, 2008.
mla: Klöpper, Benjamin, et al. “Domain Spanning Search for the Identification of
Solution Patterns for the Conceptual Design of Self-Optimizing Systems.” 2008
19th International Conference on Database and Expert Systems Applications,
2008, doi:10.1109/dexa.2008.111.
short: 'B. Klöpper, H. Podlogar, J. Gausemeier, K. Witting, in: 2008 19th International
Conference on Database and Expert Systems Applications, 2008.'
date_created: 2020-04-16T08:16:02Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1109/dexa.2008.111
publication: 2008 19th International Conference on Database and Expert Systems Applications
publication_identifier:
isbn:
- '9780769532998'
publication_status: published
status: public
title: Domain Spanning Search for the Identification of Solution Patterns for the
Conceptual Design of Self-Optimizing Systems
type: conference
user_id: '15701'
year: '2008'
...
---
_id: '21600'
abstract:
- lang: eng
text: Many problems in science and engineering require an efficient numerical approximation
of integrals or solutions to differential equations. For systems with rapidly
changing dynamics, an equidistant discretization is often inadvisable as it results
in prohibitively large errors or computational effort. To this end, adaptive schemes,
such as solvers based on Runge–Kutta pairs, have been developed which adapt the
step size based on local error estimations at each step. While the classical schemes
apply very generally and are highly efficient on regular systems, they can behave
suboptimally when an inefficient step rejection mechanism is triggered by structurally
complex systems such as chaotic systems. To overcome these issues, we propose
a method to tailor numerical schemes to the problem class at hand. This is achieved
by combining simple, classical quadrature rules or ODE solvers with data-driven
time-stepping controllers. Compared with learning solution operators to ODEs directly,
it generalizes better to unseen initial data as our approach employs classical
numerical schemes as base methods. At the same time it can make use of identified
structures of a problem class and, therefore, outperforms state-of-the-art adaptive
schemes. Several examples demonstrate superior efficiency. Source code is available
at https://github.com/lueckem/quadrature-ML.
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Eyke
full_name: Hüllermeier, Eyke
id: '48129'
last_name: Hüllermeier
- first_name: Marvin
full_name: Lücke, Marvin
last_name: Lücke
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Karlson
full_name: Pfannschmidt, Karlson
id: '13472'
last_name: Pfannschmidt
orcid: 0000-0001-9407-7903
citation:
ama: Dellnitz M, Hüllermeier E, Lücke M, et al. Efficient time stepping for numerical
integration using reinforcement learning. SIAM Journal on Scientific Computing.
2023;45(2):A579-A595. doi:10.1137/21M1412682
apa: Dellnitz, M., Hüllermeier, E., Lücke, M., Ober-Blöbaum, S., Offen, C., Peitz,
S., & Pfannschmidt, K. (2023). Efficient time stepping for numerical integration
using reinforcement learning. SIAM Journal on Scientific Computing, 45(2),
A579–A595. https://doi.org/10.1137/21M1412682
bibtex: '@article{Dellnitz_Hüllermeier_Lücke_Ober-Blöbaum_Offen_Peitz_Pfannschmidt_2023,
title={Efficient time stepping for numerical integration using reinforcement
learning}, volume={45}, DOI={10.1137/21M1412682},
number={2}, journal={SIAM Journal on Scientific Computing}, author={Dellnitz,
Michael and Hüllermeier, Eyke and Lücke, Marvin and Ober-Blöbaum, Sina and Offen,
Christian and Peitz, Sebastian and Pfannschmidt, Karlson}, year={2023}, pages={A579–A595}
}'
chicago: 'Dellnitz, Michael, Eyke Hüllermeier, Marvin Lücke, Sina Ober-Blöbaum,
Christian Offen, Sebastian Peitz, and Karlson Pfannschmidt. “Efficient Time Stepping
for Numerical Integration Using Reinforcement Learning.” SIAM Journal on Scientific
Computing 45, no. 2 (2023): A579–95. https://doi.org/10.1137/21M1412682.'
ieee: 'M. Dellnitz et al., “Efficient time stepping for numerical integration
using reinforcement learning,” SIAM Journal on Scientific Computing, vol.
45, no. 2, pp. A579–A595, 2023, doi: 10.1137/21M1412682.'
mla: Dellnitz, Michael, et al. “Efficient Time Stepping for Numerical Integration
Using Reinforcement Learning.” SIAM Journal on Scientific Computing, vol.
45, no. 2, 2023, pp. A579–95, doi:10.1137/21M1412682.
short: M. Dellnitz, E. Hüllermeier, M. Lücke, S. Ober-Blöbaum, C. Offen, S. Peitz,
K. Pfannschmidt, SIAM Journal on Scientific Computing 45 (2023) A579–A595.
date_created: 2021-04-09T07:59:19Z
date_updated: 2023-08-25T09:24:50Z
ddc:
- '510'
department:
- _id: '101'
- _id: '636'
- _id: '355'
- _id: '655'
doi: 10.1137/21M1412682
external_id:
arxiv:
- arXiv:2104.03562
has_accepted_license: '1'
intvolume: ' 45'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/reader/10.1137/21M1412682
page: A579-A595
publication: SIAM Journal on Scientific Computing
publication_status: published
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/lueckem/quadrature-ML
status: public
title: Efficient time stepping for numerical integration using reinforcement learning
type: journal_article
user_id: '47427'
volume: 45
year: '2023'
...
---
_id: '30294'
abstract:
- lang: eng
text: With the ever increasing capabilities of sensors and controllers, autonomous
driving is quickly becoming a reality. This disruptive change in the automotive
industry poses major challenges for manufacturers as well as suppliers as entirely
new design and testing strategies have to be developed to remain competitive.
Most importantly, the complexity of autonomously driving vehicles in a complex,
uncertain, and safety-critical environment requires new testing procedures to
cover the almost infinite range of potential scenarios.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Sebastian
full_name: Bannenberg, Sebastian
last_name: Bannenberg
citation:
ama: 'Peitz S, Dellnitz M, Bannenberg S. Efficient Virtual Design and Testing of
Autonomous Vehicles. In: Bock HG, Küfer K-H, Maas P, Milde A, Schulz V, eds. German
Success Stories in Industrial Mathematics. Vol 35. Mathematics in Industry.
Springer International Publishing; 2022. doi:10.1007/978-3-030-81455-7_23'
apa: Peitz, S., Dellnitz, M., & Bannenberg, S. (2022). Efficient Virtual Design
and Testing of Autonomous Vehicles. In H. G. Bock, K.-H. Küfer, P. Maas, A. Milde,
& V. Schulz (Eds.), German Success Stories in Industrial Mathematics
(Vol. 35). Springer International Publishing. https://doi.org/10.1007/978-3-030-81455-7_23
bibtex: '@inbook{Peitz_Dellnitz_Bannenberg_2022, place={Cham}, series={Mathematics
in Industry}, title={Efficient Virtual Design and Testing of Autonomous Vehicles},
volume={35}, DOI={10.1007/978-3-030-81455-7_23},
booktitle={German Success Stories in Industrial Mathematics}, publisher={Springer
International Publishing}, author={Peitz, Sebastian and Dellnitz, Michael and
Bannenberg, Sebastian}, editor={Bock, H. G. and Küfer, K.-H. and Maas, P. and
Milde, A. and Schulz, V.}, year={2022}, collection={Mathematics in Industry} }'
chicago: 'Peitz, Sebastian, Michael Dellnitz, and Sebastian Bannenberg. “Efficient
Virtual Design and Testing of Autonomous Vehicles.” In German Success Stories
in Industrial Mathematics, edited by H. G. Bock, K.-H. Küfer, P. Maas, A.
Milde, and V. Schulz, Vol. 35. Mathematics in Industry. Cham: Springer International
Publishing, 2022. https://doi.org/10.1007/978-3-030-81455-7_23.'
ieee: 'S. Peitz, M. Dellnitz, and S. Bannenberg, “Efficient Virtual Design and Testing
of Autonomous Vehicles,” in German Success Stories in Industrial Mathematics,
vol. 35, H. G. Bock, K.-H. Küfer, P. Maas, A. Milde, and V. Schulz, Eds. Cham:
Springer International Publishing, 2022.'
mla: Peitz, Sebastian, et al. “Efficient Virtual Design and Testing of Autonomous
Vehicles.” German Success Stories in Industrial Mathematics, edited by
H. G. Bock et al., vol. 35, Springer International Publishing, 2022, doi:10.1007/978-3-030-81455-7_23.
short: 'S. Peitz, M. Dellnitz, S. Bannenberg, in: H.G. Bock, K.-H. Küfer, P. Maas,
A. Milde, V. Schulz (Eds.), German Success Stories in Industrial Mathematics,
Springer International Publishing, Cham, 2022.'
date_created: 2022-03-14T07:32:41Z
date_updated: 2022-03-14T07:42:01Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/978-3-030-81455-7_23
editor:
- first_name: H. G.
full_name: Bock, H. G.
last_name: Bock
- first_name: K.-H.
full_name: Küfer, K.-H.
last_name: Küfer
- first_name: P.
full_name: Maas, P.
last_name: Maas
- first_name: A.
full_name: Milde, A.
last_name: Milde
- first_name: V.
full_name: Schulz, V.
last_name: Schulz
intvolume: ' 35'
language:
- iso: eng
place: Cham
publication: German Success Stories in Industrial Mathematics
publication_identifier:
isbn:
- '9783030814540'
- '9783030814557'
issn:
- 1612-3956
- 2198-3283
publication_status: published
publisher: Springer International Publishing
series_title: Mathematics in Industry
status: public
title: Efficient Virtual Design and Testing of Autonomous Vehicles
type: book_chapter
user_id: '47427'
volume: 35
year: '2022'
...
---
_id: '16544'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Jürgen
full_name: Scheurle, Jürgen
last_name: Scheurle
citation:
ama: 'Dellnitz M, Scheurle J. Eigenvalue Movement for a Class of Reversible Hamiltonian
Systems with Three Degrees of Freedom. In: Dynamics, Bifurcation and Symmetry.
Dordrecht; 1994. doi:10.1007/978-94-011-0956-7_9'
apa: Dellnitz, M., & Scheurle, J. (1994). Eigenvalue Movement for a Class of
Reversible Hamiltonian Systems with Three Degrees of Freedom. In Dynamics,
Bifurcation and Symmetry. Dordrecht. https://doi.org/10.1007/978-94-011-0956-7_9
bibtex: '@inbook{Dellnitz_Scheurle_1994, place={Dordrecht}, title={Eigenvalue Movement
for a Class of Reversible Hamiltonian Systems with Three Degrees of Freedom},
DOI={10.1007/978-94-011-0956-7_9},
booktitle={Dynamics, Bifurcation and Symmetry}, author={Dellnitz, Michael and
Scheurle, Jürgen}, year={1994} }'
chicago: Dellnitz, Michael, and Jürgen Scheurle. “Eigenvalue Movement for a Class
of Reversible Hamiltonian Systems with Three Degrees of Freedom.” In Dynamics,
Bifurcation and Symmetry. Dordrecht, 1994. https://doi.org/10.1007/978-94-011-0956-7_9.
ieee: M. Dellnitz and J. Scheurle, “Eigenvalue Movement for a Class of Reversible
Hamiltonian Systems with Three Degrees of Freedom,” in Dynamics, Bifurcation
and Symmetry, Dordrecht, 1994.
mla: Dellnitz, Michael, and Jürgen Scheurle. “Eigenvalue Movement for a Class of
Reversible Hamiltonian Systems with Three Degrees of Freedom.” Dynamics, Bifurcation
and Symmetry, 1994, doi:10.1007/978-94-011-0956-7_9.
short: 'M. Dellnitz, J. Scheurle, in: Dynamics, Bifurcation and Symmetry, Dordrecht,
1994.'
date_created: 2020-04-15T08:53:18Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-94-011-0956-7_9
language:
- iso: eng
place: Dordrecht
publication: Dynamics, Bifurcation and Symmetry
publication_identifier:
isbn:
- '9789401044134'
- '9789401109567'
publication_status: published
status: public
title: Eigenvalue Movement for a Class of Reversible Hamiltonian Systems with Three
Degrees of Freedom
type: book_chapter
user_id: '15701'
year: '1994'
...
---
_id: '21195'
author:
- first_name: Christian
full_name: Goelz, Christian
last_name: Goelz
- first_name: Karin
full_name: Mora, Karin
last_name: Mora
- first_name: Julia Kristin
full_name: Stroehlein, Julia Kristin
last_name: Stroehlein
- first_name: Franziska Katharina
full_name: Haase, Franziska Katharina
last_name: Haase
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Claus
full_name: Reinsberger, Claus
last_name: Reinsberger
- first_name: Solveig
full_name: Vieluf, Solveig
last_name: Vieluf
citation:
ama: Goelz C, Mora K, Stroehlein JK, et al. Electrophysiological signatures of dedifferentiation
differ between fit and less fit older adults. Cognitive Neurodynamics.
2021. doi:10.1007/s11571-020-09656-9
apa: Goelz, C., Mora, K., Stroehlein, J. K., Haase, F. K., Dellnitz, M., Reinsberger,
C., & Vieluf, S. (2021). Electrophysiological signatures of dedifferentiation
differ between fit and less fit older adults. Cognitive Neurodynamics.
https://doi.org/10.1007/s11571-020-09656-9
bibtex: '@article{Goelz_Mora_Stroehlein_Haase_Dellnitz_Reinsberger_Vieluf_2021,
title={Electrophysiological signatures of dedifferentiation differ between fit
and less fit older adults}, DOI={10.1007/s11571-020-09656-9},
journal={Cognitive Neurodynamics}, author={Goelz, Christian and Mora, Karin and
Stroehlein, Julia Kristin and Haase, Franziska Katharina and Dellnitz, Michael
and Reinsberger, Claus and Vieluf, Solveig}, year={2021} }'
chicago: Goelz, Christian, Karin Mora, Julia Kristin Stroehlein, Franziska Katharina
Haase, Michael Dellnitz, Claus Reinsberger, and Solveig Vieluf. “Electrophysiological
Signatures of Dedifferentiation Differ between Fit and Less Fit Older Adults.”
Cognitive Neurodynamics, 2021. https://doi.org/10.1007/s11571-020-09656-9.
ieee: C. Goelz et al., “Electrophysiological signatures of dedifferentiation
differ between fit and less fit older adults,” Cognitive Neurodynamics,
2021.
mla: Goelz, Christian, et al. “Electrophysiological Signatures of Dedifferentiation
Differ between Fit and Less Fit Older Adults.” Cognitive Neurodynamics,
2021, doi:10.1007/s11571-020-09656-9.
short: C. Goelz, K. Mora, J.K. Stroehlein, F.K. Haase, M. Dellnitz, C. Reinsberger,
S. Vieluf, Cognitive Neurodynamics (2021).
date_created: 2021-02-08T13:16:07Z
date_updated: 2022-01-06T06:54:49Z
department:
- _id: '101'
doi: 10.1007/s11571-020-09656-9
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/content/pdf/10.1007/s11571-020-09656-9.pdf
publication: Cognitive Neurodynamics
status: public
title: Electrophysiological signatures of dedifferentiation differ between fit and
less fit older adults
type: journal_article
user_id: '32643'
year: '2021'
...
---
_id: '16589'
author:
- first_name: K.
full_name: Flaskamp, K.
last_name: Flaskamp
- first_name: S.
full_name: Ober-Blobaum, S.
last_name: Ober-Blobaum
citation:
ama: 'Flaskamp K, Ober-Blobaum S. Energy efficient control for mechanical systems
based on inherent dynamical structures. In: 2012 American Control Conference
(ACC). ; 2012. doi:10.1109/acc.2012.6314820'
apa: Flaskamp, K., & Ober-Blobaum, S. (2012). Energy efficient control for mechanical
systems based on inherent dynamical structures. In 2012 American Control Conference
(ACC). https://doi.org/10.1109/acc.2012.6314820
bibtex: '@inproceedings{Flaskamp_Ober-Blobaum_2012, title={Energy efficient control
for mechanical systems based on inherent dynamical structures}, DOI={10.1109/acc.2012.6314820},
booktitle={2012 American Control Conference (ACC)}, author={Flaskamp, K. and Ober-Blobaum,
S.}, year={2012} }'
chicago: Flaskamp, K., and S. Ober-Blobaum. “Energy Efficient Control for Mechanical
Systems Based on Inherent Dynamical Structures.” In 2012 American Control Conference
(ACC), 2012. https://doi.org/10.1109/acc.2012.6314820.
ieee: K. Flaskamp and S. Ober-Blobaum, “Energy efficient control for mechanical
systems based on inherent dynamical structures,” in 2012 American Control Conference
(ACC), 2012.
mla: Flaskamp, K., and S. Ober-Blobaum. “Energy Efficient Control for Mechanical
Systems Based on Inherent Dynamical Structures.” 2012 American Control Conference
(ACC), 2012, doi:10.1109/acc.2012.6314820.
short: 'K. Flaskamp, S. Ober-Blobaum, in: 2012 American Control Conference (ACC),
2012.'
date_created: 2020-04-16T05:49:41Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1109/acc.2012.6314820
language:
- iso: eng
publication: 2012 American Control Conference (ACC)
publication_identifier:
isbn:
- '9781457710964'
- '9781457710957'
- '9781457710940'
- '9781467321020'
publication_status: published
status: public
title: Energy efficient control for mechanical systems based on inherent dynamical
structures
type: conference
user_id: '15701'
year: '2012'
...
---
_id: '16626'
author:
- first_name: Tobias
full_name: Knoke, Tobias
last_name: Knoke
- first_name: Christoph
full_name: Romaus, Christoph
last_name: Romaus
- first_name: Joachim
full_name: Bocker, Joachim
last_name: Bocker
- first_name: Alessandro
full_name: Dell'Aere, Alessandro
last_name: Dell'Aere
- first_name: Katrin
full_name: Witting, Katrin
last_name: Witting
citation:
ama: 'Knoke T, Romaus C, Bocker J, Dell’Aere A, Witting K. Energy Management for
an Onboard Storage System Based on Multi-Objective Optimization. In: IECON
2006 - 32nd Annual Conference on IEEE Industrial Electronics. ; 2006. doi:10.1109/iecon.2006.347705'
apa: Knoke, T., Romaus, C., Bocker, J., Dell’Aere, A., & Witting, K. (2006).
Energy Management for an Onboard Storage System Based on Multi-Objective Optimization.
In IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics.
https://doi.org/10.1109/iecon.2006.347705
bibtex: '@inproceedings{Knoke_Romaus_Bocker_Dell’Aere_Witting_2006, title={Energy
Management for an Onboard Storage System Based on Multi-Objective Optimization},
DOI={10.1109/iecon.2006.347705},
booktitle={IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics},
author={Knoke, Tobias and Romaus, Christoph and Bocker, Joachim and Dell’Aere,
Alessandro and Witting, Katrin}, year={2006} }'
chicago: Knoke, Tobias, Christoph Romaus, Joachim Bocker, Alessandro Dell’Aere,
and Katrin Witting. “Energy Management for an Onboard Storage System Based on
Multi-Objective Optimization.” In IECON 2006 - 32nd Annual Conference on IEEE
Industrial Electronics, 2006. https://doi.org/10.1109/iecon.2006.347705.
ieee: T. Knoke, C. Romaus, J. Bocker, A. Dell’Aere, and K. Witting, “Energy Management
for an Onboard Storage System Based on Multi-Objective Optimization,” in IECON
2006 - 32nd Annual Conference on IEEE Industrial Electronics, 2006.
mla: Knoke, Tobias, et al. “Energy Management for an Onboard Storage System Based
on Multi-Objective Optimization.” IECON 2006 - 32nd Annual Conference on IEEE
Industrial Electronics, 2006, doi:10.1109/iecon.2006.347705.
short: 'T. Knoke, C. Romaus, J. Bocker, A. Dell’Aere, K. Witting, in: IECON 2006
- 32nd Annual Conference on IEEE Industrial Electronics, 2006.'
date_created: 2020-04-16T08:20:27Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1109/iecon.2006.347705
language:
- iso: eng
publication: IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics
publication_identifier:
isbn:
- '1424403901'
- 142440391X
issn:
- 1553-572X
publication_status: published
status: public
title: Energy Management for an Onboard Storage System Based on Multi-Objective Optimization
type: conference
user_id: '15701'
year: '2006'
...
---
_id: '16663'
author:
- first_name: T.
full_name: Schneider, T.
last_name: Schneider
- first_name: B.
full_name: Schulz, B.
last_name: Schulz
- first_name: C.
full_name: Henke, C.
last_name: Henke
- first_name: K.
full_name: Witting, K.
last_name: Witting
- first_name: D.
full_name: Steenken, D.
last_name: Steenken
- first_name: J.
full_name: Bocker, J.
last_name: Bocker
citation:
ama: 'Schneider T, Schulz B, Henke C, Witting K, Steenken D, Bocker J. Energy transfer
via linear doubly-fed motor in different operating modes. In: 2009 IEEE International
Electric Machines and Drives Conference. ; 2009. doi:10.1109/iemdc.2009.5075267'
apa: Schneider, T., Schulz, B., Henke, C., Witting, K., Steenken, D., & Bocker,
J. (2009). Energy transfer via linear doubly-fed motor in different operating
modes. In 2009 IEEE International Electric Machines and Drives Conference.
https://doi.org/10.1109/iemdc.2009.5075267
bibtex: '@inproceedings{Schneider_Schulz_Henke_Witting_Steenken_Bocker_2009, title={Energy
transfer via linear doubly-fed motor in different operating modes}, DOI={10.1109/iemdc.2009.5075267},
booktitle={2009 IEEE International Electric Machines and Drives Conference}, author={Schneider,
T. and Schulz, B. and Henke, C. and Witting, K. and Steenken, D. and Bocker, J.},
year={2009} }'
chicago: Schneider, T., B. Schulz, C. Henke, K. Witting, D. Steenken, and J. Bocker.
“Energy Transfer via Linear Doubly-Fed Motor in Different Operating Modes.” In
2009 IEEE International Electric Machines and Drives Conference, 2009.
https://doi.org/10.1109/iemdc.2009.5075267.
ieee: T. Schneider, B. Schulz, C. Henke, K. Witting, D. Steenken, and J. Bocker,
“Energy transfer via linear doubly-fed motor in different operating modes,” in
2009 IEEE International Electric Machines and Drives Conference, 2009.
mla: Schneider, T., et al. “Energy Transfer via Linear Doubly-Fed Motor in Different
Operating Modes.” 2009 IEEE International Electric Machines and Drives Conference,
2009, doi:10.1109/iemdc.2009.5075267.
short: 'T. Schneider, B. Schulz, C. Henke, K. Witting, D. Steenken, J. Bocker, in:
2009 IEEE International Electric Machines and Drives Conference, 2009.'
date_created: 2020-04-16T09:56:21Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1109/iemdc.2009.5075267
publication: 2009 IEEE International Electric Machines and Drives Conference
publication_identifier:
isbn:
- '9781424442515'
publication_status: published
status: public
title: Energy transfer via linear doubly-fed motor in different operating modes
type: conference
user_id: '15701'
year: '2009'
...
---
_id: '16297'
abstract:
- lang: eng
text: "In real-world problems, uncertainties (e.g., errors in the measurement,\r\nprecision
errors) often lead to poor performance of numerical algorithms when\r\nnot explicitly
taken into account. This is also the case for control problems,\r\nwhere optimal
solutions can degrade in quality or even become infeasible. Thus,\r\nthere is
the need to design methods that can handle uncertainty. In this work,\r\nwe consider
nonlinear multi-objective optimal control problems with uncertainty\r\non the
initial conditions, and in particular their incorporation into a\r\nfeedback loop
via model predictive control (MPC). In multi-objective optimal\r\ncontrol, an
optimal compromise between multiple conflicting criteria has to be\r\nfound. For
such problems, not much has been reported in terms of uncertainties.\r\nTo address
this problem class, we design an offline/online framework to compute\r\nan approximation
of efficient control strategies. This approach is closely\r\nrelated to explicit
MPC for nonlinear systems, where the potentially expensive\r\noptimization problem
is solved in an offline phase in order to enable fast\r\nsolutions in the online
phase. In order to reduce the numerical cost of the\r\noffline phase, we exploit
symmetries in the control problems. Furthermore, in\r\norder to ensure optimality
of the solutions, we include an additional online\r\noptimization step, which
is considerably cheaper than the original\r\nmulti-objective optimization problem.
We test our framework on a car\r\nmaneuvering problem where safety and speed are
the objectives. The\r\nmulti-objective framework allows for online adaptations
of the desired\r\nobjective. Alternatively, an automatic scalarizing procedure
yields very\r\nefficient feedback controls. Our results show that the method is
capable of\r\ndesigning driving strategies that deal better with uncertainties
in the initial\r\nconditions, which translates into potentially safer and faster
driving\r\nstrategies."
author:
- first_name: Carlos Ignacio
full_name: Hernández Castellanos, Carlos Ignacio
last_name: Hernández Castellanos
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: Hernández Castellanos CI, Ober-Blöbaum S, Peitz S. Explicit Multi-objective
Model Predictive Control for Nonlinear Systems Under Uncertainty. International
Journal of Robust and Nonlinear Control. 2020;30(17):7593-7618. doi:10.1002/rnc.5197
apa: Hernández Castellanos, C. I., Ober-Blöbaum, S., & Peitz, S. (2020). Explicit
Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty.
International Journal of Robust and Nonlinear Control, 30(17), 7593–7618.
https://doi.org/10.1002/rnc.5197
bibtex: '@article{Hernández Castellanos_Ober-Blöbaum_Peitz_2020, title={Explicit
Multi-objective Model Predictive Control for Nonlinear Systems Under Uncertainty},
volume={30(17)}, DOI={10.1002/rnc.5197},
journal={International Journal of Robust and Nonlinear Control}, author={Hernández
Castellanos, Carlos Ignacio and Ober-Blöbaum, Sina and Peitz, Sebastian}, year={2020},
pages={7593–7618} }'
chicago: 'Hernández Castellanos, Carlos Ignacio, Sina Ober-Blöbaum, and Sebastian
Peitz. “Explicit Multi-Objective Model Predictive Control for Nonlinear Systems
Under Uncertainty.” International Journal of Robust and Nonlinear Control
30(17) (2020): 7593–7618. https://doi.org/10.1002/rnc.5197.'
ieee: 'C. I. Hernández Castellanos, S. Ober-Blöbaum, and S. Peitz, “Explicit Multi-objective
Model Predictive Control for Nonlinear Systems Under Uncertainty,” International
Journal of Robust and Nonlinear Control, vol. 30(17), pp. 7593–7618, 2020,
doi: 10.1002/rnc.5197.'
mla: Hernández Castellanos, Carlos Ignacio, et al. “Explicit Multi-Objective Model
Predictive Control for Nonlinear Systems Under Uncertainty.” International
Journal of Robust and Nonlinear Control, vol. 30(17), 2020, pp. 7593–618,
doi:10.1002/rnc.5197.
short: C.I. Hernández Castellanos, S. Ober-Blöbaum, S. Peitz, International Journal
of Robust and Nonlinear Control 30(17) (2020) 7593–7618.
date_created: 2020-03-13T12:45:56Z
date_updated: 2022-01-21T09:55:39Z
department:
- _id: '101'
doi: 10.1002/rnc.5197
language:
- iso: eng
page: 7593-7618
publication: International Journal of Robust and Nonlinear Control
status: public
title: Explicit Multi-objective Model Predictive Control for Nonlinear Systems Under
Uncertainty
type: journal_article
user_id: '15694'
volume: 30(17)
year: '2020'
...
---
_id: '16294'
abstract:
- lang: eng
text: "Model predictive control is a prominent approach to construct a feedback\r\ncontrol
loop for dynamical systems. Due to real-time constraints, the major\r\nchallenge
in MPC is to solve model-based optimal control problems in a very\r\nshort amount
of time. For linear-quadratic problems, Bemporad et al. have\r\nproposed an explicit
formulation where the underlying optimization problems are\r\nsolved a priori
in an offline phase. In this article, we present an extension\r\nof this concept
in two significant ways. We consider nonlinear problems and -\r\nmore importantly
- problems with multiple conflicting objective functions. In\r\nthe offline phase,
we build a library of Pareto optimal solutions from which we\r\nthen obtain a
valid compromise solution in the online phase according to a\r\ndecision maker's
preference. Since the standard multi-parametric programming\r\napproach is no
longer valid in this situation, we instead use interpolation\r\nbetween different
entries of the library. To reduce the number of problems that\r\nhave to be solved
in the offline phase, we exploit symmetries in the dynamical\r\nsystem and the
corresponding multiobjective optimal control problem. The\r\nresults are verified
using two different examples from autonomous driving."
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for
nonlinear systems with symmetries. International Journal of Robust and Nonlinear
Control. 2021;31(2):380-403. doi:10.1002/rnc.5281
apa: Ober-Blöbaum, S., & Peitz, S. (2021). Explicit multiobjective model predictive
control for nonlinear systems with symmetries. International Journal of Robust
and Nonlinear Control, 31(2), 380–403. https://doi.org/10.1002/rnc.5281
bibtex: '@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model
predictive control for nonlinear systems with symmetries}, volume={31(2)}, DOI={10.1002/rnc.5281}, journal={International
Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz,
Sebastian}, year={2021}, pages={380–403} }'
chicago: 'Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model
Predictive Control for Nonlinear Systems with Symmetries.” International Journal
of Robust and Nonlinear Control 31(2) (2021): 380–403. https://doi.org/10.1002/rnc.5281.'
ieee: 'S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control
for nonlinear systems with symmetries,” International Journal of Robust and
Nonlinear Control, vol. 31(2), pp. 380–403, 2021, doi: 10.1002/rnc.5281.'
mla: Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive
Control for Nonlinear Systems with Symmetries.” International Journal of Robust
and Nonlinear Control, vol. 31(2), 2021, pp. 380–403, doi:10.1002/rnc.5281.
short: S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear
Control 31(2) (2021) 380–403.
date_created: 2020-03-13T12:44:36Z
date_updated: 2022-01-24T13:27:50Z
department:
- _id: '101'
doi: 10.1002/rnc.5281
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281
oa: '1'
page: 380-403
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: International Journal of Robust and Nonlinear Control
status: public
title: Explicit multiobjective model predictive control for nonlinear systems with
symmetries
type: journal_article
user_id: '15694'
volume: 31(2)
year: '2021'
...
---
_id: '16552'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Andreas
full_name: Hohmann, Andreas
last_name: Hohmann
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Martin
full_name: Rumpf, Martin
last_name: Rumpf
citation:
ama: 'Dellnitz M, Hohmann A, Junge O, Rumpf M. Exploring invariant sets and invariant
measures. Chaos: An Interdisciplinary Journal of Nonlinear Science. 1997:221-228.
doi:10.1063/1.166223'
apa: 'Dellnitz, M., Hohmann, A., Junge, O., & Rumpf, M. (1997). Exploring invariant
sets and invariant measures. Chaos: An Interdisciplinary Journal of Nonlinear
Science, 221–228. https://doi.org/10.1063/1.166223'
bibtex: '@article{Dellnitz_Hohmann_Junge_Rumpf_1997, title={Exploring invariant
sets and invariant measures}, DOI={10.1063/1.166223},
journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, author={Dellnitz,
Michael and Hohmann, Andreas and Junge, Oliver and Rumpf, Martin}, year={1997},
pages={221–228} }'
chicago: 'Dellnitz, Michael, Andreas Hohmann, Oliver Junge, and Martin Rumpf. “Exploring
Invariant Sets and Invariant Measures.” Chaos: An Interdisciplinary Journal
of Nonlinear Science, 1997, 221–28. https://doi.org/10.1063/1.166223.'
ieee: 'M. Dellnitz, A. Hohmann, O. Junge, and M. Rumpf, “Exploring invariant sets
and invariant measures,” Chaos: An Interdisciplinary Journal of Nonlinear Science,
pp. 221–228, 1997.'
mla: 'Dellnitz, Michael, et al. “Exploring Invariant Sets and Invariant Measures.”
Chaos: An Interdisciplinary Journal of Nonlinear Science, 1997, pp. 221–28,
doi:10.1063/1.166223.'
short: 'M. Dellnitz, A. Hohmann, O. Junge, M. Rumpf, Chaos: An Interdisciplinary
Journal of Nonlinear Science (1997) 221–228.'
date_created: 2020-04-15T09:06:28Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1063/1.166223
language:
- iso: eng
page: 221-228
publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science'
publication_identifier:
issn:
- 1054-1500
- 1089-7682
publication_status: published
status: public
title: Exploring invariant sets and invariant measures
type: journal_article
user_id: '15701'
year: '1997'
...
---
_id: '16598'
author:
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
citation:
ama: 'Froyland G. Extracting Dynamical Behavior via Markov Models. In: Nonlinear
Dynamics and Statistics. Boston, MA; 2001. doi:10.1007/978-1-4612-0177-9_12'
apa: Froyland, G. (2001). Extracting Dynamical Behavior via Markov Models. In Nonlinear
Dynamics and Statistics. Boston, MA. https://doi.org/10.1007/978-1-4612-0177-9_12
bibtex: '@inbook{Froyland_2001, place={Boston, MA}, title={Extracting Dynamical
Behavior via Markov Models}, DOI={10.1007/978-1-4612-0177-9_12},
booktitle={Nonlinear Dynamics and Statistics}, author={Froyland, Gary}, year={2001}
}'
chicago: Froyland, Gary. “Extracting Dynamical Behavior via Markov Models.” In Nonlinear
Dynamics and Statistics. Boston, MA, 2001. https://doi.org/10.1007/978-1-4612-0177-9_12.
ieee: G. Froyland, “Extracting Dynamical Behavior via Markov Models,” in Nonlinear
Dynamics and Statistics, Boston, MA, 2001.
mla: Froyland, Gary. “Extracting Dynamical Behavior via Markov Models.” Nonlinear
Dynamics and Statistics, 2001, doi:10.1007/978-1-4612-0177-9_12.
short: 'G. Froyland, in: Nonlinear Dynamics and Statistics, Boston, MA, 2001.'
date_created: 2020-04-16T06:03:45Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-1-4612-0177-9_12
language:
- iso: eng
place: Boston, MA
publication: Nonlinear Dynamics and Statistics
publication_identifier:
isbn:
- '9781461266488'
- '9781461201779'
publication_status: published
status: public
title: Extracting Dynamical Behavior via Markov Models
type: book_chapter
user_id: '15701'
year: '2001'
...
---
_id: '32447'
abstract:
- lang: eng
text: 'We present a new gradient-like dynamical system related to unconstrained
convex smooth multiobjective optimization which involves inertial effects and
asymptotic vanishing damping. To the best of our knowledge, this system is the
first inertial gradient-like system for multiobjective optimization problems including
asymptotic vanishing damping, expanding the ideas laid out in [H. Attouch and
G. Garrigos, Multiobjective optimization: an inertial approach to Pareto optima,
preprint, arXiv:1506.02823, 201]. We prove existence of solutions to this system
in finite dimensions and further prove that its bounded solutions converge weakly
to weakly Pareto optimal points. In addition, we obtain a convergence rate of
order O(t−2) for the function values measured with a merit function. This approach
presents a good basis for the development of fast gradient methods for multiobjective
optimization.'
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Sonntag K, Peitz S. Fast Convergence of Inertial Multiobjective Gradient-like
Systems with Asymptotic Vanishing Damping. arXiv:230700975. Published online
2023.
apa: Sonntag, K., & Peitz, S. (2023). Fast Convergence of Inertial Multiobjective
Gradient-like Systems with Asymptotic Vanishing Damping. In arXiv:2307.00975.
bibtex: '@article{Sonntag_Peitz_2023, title={Fast Convergence of Inertial Multiobjective
Gradient-like Systems with Asymptotic Vanishing Damping}, journal={arXiv:2307.00975},
author={Sonntag, Konstantin and Peitz, Sebastian}, year={2023} }'
chicago: Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial
Multiobjective Gradient-like Systems with Asymptotic Vanishing Damping.” ArXiv:2307.00975,
2023.
ieee: K. Sonntag and S. Peitz, “Fast Convergence of Inertial Multiobjective Gradient-like
Systems with Asymptotic Vanishing Damping,” arXiv:2307.00975. 2023.
mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Convergence of Inertial Multiobjective
Gradient-like Systems with Asymptotic Vanishing Damping.” ArXiv:2307.00975,
2023.
short: K. Sonntag, S. Peitz, ArXiv:2307.00975 (2023).
date_created: 2022-07-28T11:53:02Z
date_updated: 2024-02-21T10:15:33Z
department:
- _id: '101'
- _id: '655'
external_id:
arxiv:
- '2307.00975'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2307.00975.pdf
oa: '1'
publication: arXiv:2307.00975
status: public
title: Fast Convergence of Inertial Multiobjective Gradient-like Systems with Asymptotic
Vanishing Damping
type: preprint
user_id: '56399'
year: '2023'
...
---
_id: '46019'
abstract:
- lang: eng
text: We derive efficient algorithms to compute weakly Pareto optimal solutions
for smooth, convex and unconstrained multiobjective optimization problems in general
Hilbert spaces. To this end, we define a novel inertial gradient-like dynamical
system in the multiobjective setting, which trajectories converge weakly to Pareto
optimal solutions. Discretization of this system yields an inertial multiobjective
algorithm which generates sequences that converge weakly to Pareto optimal solutions.
We employ Nesterov acceleration to define an algorithm with an improved convergence
rate compared to the plain multiobjective steepest descent method (Algorithm 1).
A further improvement in terms of efficiency is achieved by avoiding the solution
of a quadratic subproblem to compute a common step direction for all objective
functions, which is usually required in first-order methods. Using a different
discretization of our inertial gradient-like dynamical system, we obtain an accelerated
multiobjective gradient method that does not require the solution of a subproblem
in each step (Algorithm 2). While this algorithm does not converge in general,
it yields good results on test problems while being faster than standard steepest
descent.
author:
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Sonntag K, Peitz S. Fast Multiobjective Gradient Methods with Nesterov Acceleration
via Inertial Gradient-Like Systems. Journal of Optimization Theory and Applications.
Published online 2024. doi:10.1007/s10957-024-02389-3
apa: Sonntag, K., & Peitz, S. (2024). Fast Multiobjective Gradient Methods with
Nesterov Acceleration via Inertial Gradient-Like Systems. Journal of Optimization
Theory and Applications. https://doi.org/10.1007/s10957-024-02389-3
bibtex: '@article{Sonntag_Peitz_2024, title={Fast Multiobjective Gradient Methods
with Nesterov Acceleration via Inertial Gradient-Like Systems}, DOI={10.1007/s10957-024-02389-3},
journal={Journal of Optimization Theory and Applications}, publisher={Springer},
author={Sonntag, Konstantin and Peitz, Sebastian}, year={2024} }'
chicago: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient
Methods with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal
of Optimization Theory and Applications, 2024. https://doi.org/10.1007/s10957-024-02389-3.
ieee: 'K. Sonntag and S. Peitz, “Fast Multiobjective Gradient Methods with Nesterov
Acceleration via Inertial Gradient-Like Systems,” Journal of Optimization Theory
and Applications, 2024, doi: 10.1007/s10957-024-02389-3.'
mla: Sonntag, Konstantin, and Sebastian Peitz. “Fast Multiobjective Gradient Methods
with Nesterov Acceleration via Inertial Gradient-Like Systems.” Journal of
Optimization Theory and Applications, Springer, 2024, doi:10.1007/s10957-024-02389-3.
short: K. Sonntag, S. Peitz, Journal of Optimization Theory and Applications (2024).
date_created: 2023-07-12T06:35:58Z
date_updated: 2024-02-21T10:13:33Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s10957-024-02389-3
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10957-024-02389-3.pdf
oa: '1'
publication: Journal of Optimization Theory and Applications
publication_status: published
publisher: Springer
status: public
title: Fast Multiobjective Gradient Methods with Nesterov Acceleration via Inertial
Gradient-Like Systems
type: journal_article
user_id: '56399'
year: '2024'
...
---
_id: '16289'
abstract:
- lang: eng
text: In the development of model predictive controllers for PDE-constrained problems,
the use of reduced order models is essential to enable real-time applicability.
Besides local linearization approaches, proper orthogonal decomposition (POD)
has been most widely used in the past in order to derive such models. Due to the
huge advances concerning both theory as well as the numerical approximation, a
very promising alternative based on the Koopman operator has recently emerged.
In this chapter, we present two control strategies for model predictive control
of nonlinear PDEs using data-efficient approximations of the Koopman operator.
In the first one, the dynamic control system is replaced by a small number of
autonomous systems with different yet constant inputs. The control problem is
consequently transformed into a switching problem. In the second approach, a bilinear
surrogate model is obtained via a convex combination of these autonomous systems.
Using a recent convergence result for extended dynamic mode decomposition (EDMD),
convergence of the reduced objective function can be shown. We study the properties
of these two strategies with respect to solution quality, data requirements, and
complexity of the resulting optimization problem using the 1-dimensional Burgers
equation and the 2-dimensional Navier–Stokes equations as examples. Finally, an
extension for online adaptivity is presented.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
citation:
ama: 'Peitz S, Klus S. Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced
Order Models Based on the Koopman Operator. In: Lecture Notes in Control and
Information Sciences. Vol 484. Lecture Notes in Control and Information Sciences.
Cham: Springer; 2020:257-282. doi:10.1007/978-3-030-35713-9_10'
apa: 'Peitz, S., & Klus, S. (2020). Feedback Control of Nonlinear PDEs Using
Data-Efficient Reduced Order Models Based on the Koopman Operator. In Lecture
Notes in Control and Information Sciences (Vol. 484, pp. 257–282). Cham: Springer.
https://doi.org/10.1007/978-3-030-35713-9_10'
bibtex: '@inbook{Peitz_Klus_2020, place={Cham}, series={Lecture Notes in Control
and Information Sciences}, title={Feedback Control of Nonlinear PDEs Using Data-Efficient
Reduced Order Models Based on the Koopman Operator}, volume={484}, DOI={10.1007/978-3-030-35713-9_10},
booktitle={Lecture Notes in Control and Information Sciences}, publisher={Springer},
author={Peitz, Sebastian and Klus, Stefan}, year={2020}, pages={257–282}, collection={Lecture
Notes in Control and Information Sciences} }'
chicago: 'Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs
Using Data-Efficient Reduced Order Models Based on the Koopman Operator.” In Lecture
Notes in Control and Information Sciences, 484:257–82. Lecture Notes in Control
and Information Sciences. Cham: Springer, 2020. https://doi.org/10.1007/978-3-030-35713-9_10.'
ieee: 'S. Peitz and S. Klus, “Feedback Control of Nonlinear PDEs Using Data-Efficient
Reduced Order Models Based on the Koopman Operator,” in Lecture Notes in Control
and Information Sciences, vol. 484, Cham: Springer, 2020, pp. 257–282.'
mla: Peitz, Sebastian, and Stefan Klus. “Feedback Control of Nonlinear PDEs Using
Data-Efficient Reduced Order Models Based on the Koopman Operator.” Lecture
Notes in Control and Information Sciences, vol. 484, Springer, 2020, pp. 257–82,
doi:10.1007/978-3-030-35713-9_10.
short: 'S. Peitz, S. Klus, in: Lecture Notes in Control and Information Sciences,
Springer, Cham, 2020, pp. 257–282.'
date_created: 2020-03-13T12:38:52Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/978-3-030-35713-9_10
intvolume: ' 484'
language:
- iso: eng
page: 257-282
place: Cham
publication: Lecture Notes in Control and Information Sciences
publication_identifier:
isbn:
- '9783030357122'
- '9783030357139'
issn:
- 0170-8643
- 1610-7411
publication_status: published
publisher: Springer
series_title: Lecture Notes in Control and Information Sciences
status: public
title: Feedback Control of Nonlinear PDEs Using Data-Efficient Reduced Order Models
Based on the Koopman Operator
type: book_chapter
user_id: '47427'
volume: 484
year: '2020'
...
---
_id: '16556'
author:
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
citation:
ama: Dellnitz M. Finding zeros by multilevel subdivision techniques. IMA Journal
of Numerical Analysis. 2002:167-185. doi:10.1093/imanum/22.2.167
apa: Dellnitz, M. (2002). Finding zeros by multilevel subdivision techniques. IMA
Journal of Numerical Analysis, 167–185. https://doi.org/10.1093/imanum/22.2.167
bibtex: '@article{Dellnitz_2002, title={Finding zeros by multilevel subdivision
techniques}, DOI={10.1093/imanum/22.2.167},
journal={IMA Journal of Numerical Analysis}, author={Dellnitz, M.}, year={2002},
pages={167–185} }'
chicago: Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” IMA
Journal of Numerical Analysis, 2002, 167–85. https://doi.org/10.1093/imanum/22.2.167.
ieee: M. Dellnitz, “Finding zeros by multilevel subdivision techniques,” IMA
Journal of Numerical Analysis, pp. 167–185, 2002.
mla: Dellnitz, M. “Finding Zeros by Multilevel Subdivision Techniques.” IMA Journal
of Numerical Analysis, 2002, pp. 167–85, doi:10.1093/imanum/22.2.167.
short: M. Dellnitz, IMA Journal of Numerical Analysis (2002) 167–185.
date_created: 2020-04-15T09:12:17Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1093/imanum/22.2.167
language:
- iso: eng
page: 167-185
publication: IMA Journal of Numerical Analysis
publication_identifier:
issn:
- 0272-4979
- 1464-3642
publication_status: published
status: public
title: Finding zeros by multilevel subdivision techniques
type: journal_article
user_id: '15701'
year: '2002'
...
---
_id: '10597'
abstract:
- lang: eng
text: In comparison to classical control approaches in the field of electrical drives
like the field-oriented control (FOC), model predictive control (MPC) approaches
are able to provide a higher control performance. This refers to shorter settling
times, lower overshoots, and a better decoupling of control variables in case
of multi-variable controls. However, this can only be achieved if the used prediction
model covers the actual behavior of the plant sufficiently well. In case of model
deviations, the performance utilizing MPC remains below its potential. This results
in effects like increased current ripple or steady state setpoint deviations.
In order to achieve a high control performance, it is therefore necessary to adapt
the model to the real plant behavior. When using an online system identification,
a less accurate model is sufficient for commissioning of the drive system. In
this paper, the combination of a finite-control-set MPC (FCS-MPC) with a system
identification is proposed. The method does not require high-frequency signal
injection, but uses the measured values already required for the FCS-MPC. An evaluation
of the least squares-based identification on a laboratory test bench showed that
the model accuracy and thus the control performance could be improved by an online
update of the prediction models.
author:
- first_name: Soren
full_name: Hanke, Soren
last_name: Hanke
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Oliver
full_name: Wallscheid, Oliver
last_name: Wallscheid
- first_name: Joachim
full_name: Böcker, Joachim
last_name: Böcker
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Hanke S, Peitz S, Wallscheid O, Böcker J, Dellnitz M. Finite-Control-Set Model
Predictive Control for a Permanent Magnet Synchronous Motor Application with Online
Least Squares System Identification. In: 2019 IEEE International Symposium
on Predictive Control of Electrical Drives and Power Electronics (PRECEDE).
; 2019. doi:10.1109/precede.2019.8753313'
apa: Hanke, S., Peitz, S., Wallscheid, O., Böcker, J., & Dellnitz, M. (2019).
Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous
Motor Application with Online Least Squares System Identification. In 2019
IEEE International Symposium on Predictive Control of Electrical Drives and Power
Electronics (PRECEDE). https://doi.org/10.1109/precede.2019.8753313
bibtex: '@inproceedings{Hanke_Peitz_Wallscheid_Böcker_Dellnitz_2019, title={Finite-Control-Set
Model Predictive Control for a Permanent Magnet Synchronous Motor Application
with Online Least Squares System Identification}, DOI={10.1109/precede.2019.8753313},
booktitle={2019 IEEE International Symposium on Predictive Control of Electrical
Drives and Power Electronics (PRECEDE)}, author={Hanke, Soren and Peitz, Sebastian
and Wallscheid, Oliver and Böcker, Joachim and Dellnitz, Michael}, year={2019}
}'
chicago: Hanke, Soren, Sebastian Peitz, Oliver Wallscheid, Joachim Böcker, and Michael
Dellnitz. “Finite-Control-Set Model Predictive Control for a Permanent Magnet
Synchronous Motor Application with Online Least Squares System Identification.”
In 2019 IEEE International Symposium on Predictive Control of Electrical Drives
and Power Electronics (PRECEDE), 2019. https://doi.org/10.1109/precede.2019.8753313.
ieee: S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, and M. Dellnitz, “Finite-Control-Set
Model Predictive Control for a Permanent Magnet Synchronous Motor Application
with Online Least Squares System Identification,” in 2019 IEEE International
Symposium on Predictive Control of Electrical Drives and Power Electronics (PRECEDE),
2019.
mla: Hanke, Soren, et al. “Finite-Control-Set Model Predictive Control for a Permanent
Magnet Synchronous Motor Application with Online Least Squares System Identification.”
2019 IEEE International Symposium on Predictive Control of Electrical Drives
and Power Electronics (PRECEDE), 2019, doi:10.1109/precede.2019.8753313.
short: 'S. Hanke, S. Peitz, O. Wallscheid, J. Böcker, M. Dellnitz, in: 2019 IEEE
International Symposium on Predictive Control of Electrical Drives and Power Electronics
(PRECEDE), 2019.'
date_created: 2019-07-10T08:15:23Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1109/precede.2019.8753313
language:
- iso: eng
publication: 2019 IEEE International Symposium on Predictive Control of Electrical
Drives and Power Electronics (PRECEDE)
publication_identifier:
isbn:
- '9781538694145'
publication_status: published
status: public
title: Finite-Control-Set Model Predictive Control for a Permanent Magnet Synchronous
Motor Application with Online Least Squares System Identification
type: conference
user_id: '47427'
year: '2019'
...
---
_id: '23428'
abstract:
- lang: eng
text: "The Koopman operator has become an essential tool for data-driven approximation
of dynamical (control) systems in recent years, e.g., via extended dynamic mode
decomposition. Despite its popularity, convergence results and, in particular,
error bounds are still quite scarce. In this paper, we derive probabilistic bounds
for the approximation error and the prediction error depending on the number of
training data points; for both ordinary and stochastic differential equations.
Moreover, we extend our analysis to nonlinear control-affine systems using either
ergodic trajectories or i.i.d.\r\nsamples. Here, we exploit the linearity of the
Koopman generator to obtain a bilinear system and, thus, circumvent the curse
of dimensionality since we do not autonomize the system by augmenting the state
by the control inputs. To the\r\nbest of our knowledge, this is the first finite-data
error analysis in the stochastic and/or control setting. Finally, we demonstrate
the effectiveness of the proposed approach by comparing it with state-of-the-art
techniques showing its superiority whenever state and control are coupled."
article_number: '14'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Friedrich
full_name: Philipp, Friedrich
last_name: Philipp
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Nüske F, Peitz S, Philipp F, Schaller M, Worthmann K. Finite-data error bounds
for Koopman-based prediction and control. Journal of Nonlinear Science.
2023;33. doi:10.1007/s00332-022-09862-1
apa: Nüske, F., Peitz, S., Philipp, F., Schaller, M., & Worthmann, K. (2023).
Finite-data error bounds for Koopman-based prediction and control. Journal
of Nonlinear Science, 33, Article 14. https://doi.org/10.1007/s00332-022-09862-1
bibtex: '@article{Nüske_Peitz_Philipp_Schaller_Worthmann_2023, title={Finite-data
error bounds for Koopman-based prediction and control}, volume={33}, DOI={10.1007/s00332-022-09862-1},
number={14}, journal={Journal of Nonlinear Science}, author={Nüske, Feliks and
Peitz, Sebastian and Philipp, Friedrich and Schaller, Manuel and Worthmann, Karl},
year={2023} }'
chicago: Nüske, Feliks, Sebastian Peitz, Friedrich Philipp, Manuel Schaller, and
Karl Worthmann. “Finite-Data Error Bounds for Koopman-Based Prediction and Control.”
Journal of Nonlinear Science 33 (2023). https://doi.org/10.1007/s00332-022-09862-1.
ieee: 'F. Nüske, S. Peitz, F. Philipp, M. Schaller, and K. Worthmann, “Finite-data
error bounds for Koopman-based prediction and control,” Journal of Nonlinear
Science, vol. 33, Art. no. 14, 2023, doi: 10.1007/s00332-022-09862-1.'
mla: Nüske, Feliks, et al. “Finite-Data Error Bounds for Koopman-Based Prediction
and Control.” Journal of Nonlinear Science, vol. 33, 14, 2023, doi:10.1007/s00332-022-09862-1.
short: F. Nüske, S. Peitz, F. Philipp, M. Schaller, K. Worthmann, Journal of Nonlinear
Science 33 (2023).
date_created: 2021-08-17T12:25:09Z
date_updated: 2023-08-24T07:50:12Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s00332-022-09862-1
intvolume: ' 33'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s00332-022-09862-1.pdf
oa: '1'
publication: Journal of Nonlinear Science
publication_status: published
status: public
title: Finite-data error bounds for Koopman-based prediction and control
type: journal_article
user_id: '47427'
volume: 33
year: '2023'
...
---
_id: '16548'
author:
- first_name: M
full_name: Dellnitz, M
last_name: Dellnitz
- first_name: I
full_name: Melbourne, I
last_name: Melbourne
- first_name: J E
full_name: Marsden, J E
last_name: Marsden
citation:
ama: Dellnitz M, Melbourne I, Marsden JE. Generic bifurcation of Hamiltonian vector
fields with symmetry. Nonlinearity. 1992:979-996. doi:10.1088/0951-7715/5/4/008
apa: Dellnitz, M., Melbourne, I., & Marsden, J. E. (1992). Generic bifurcation
of Hamiltonian vector fields with symmetry. Nonlinearity, 979–996. https://doi.org/10.1088/0951-7715/5/4/008
bibtex: '@article{Dellnitz_Melbourne_Marsden_1992, title={Generic bifurcation of
Hamiltonian vector fields with symmetry}, DOI={10.1088/0951-7715/5/4/008},
journal={Nonlinearity}, author={Dellnitz, M and Melbourne, I and Marsden, J E},
year={1992}, pages={979–996} }'
chicago: Dellnitz, M, I Melbourne, and J E Marsden. “Generic Bifurcation of Hamiltonian
Vector Fields with Symmetry.” Nonlinearity, 1992, 979–96. https://doi.org/10.1088/0951-7715/5/4/008.
ieee: M. Dellnitz, I. Melbourne, and J. E. Marsden, “Generic bifurcation of Hamiltonian
vector fields with symmetry,” Nonlinearity, pp. 979–996, 1992.
mla: Dellnitz, M., et al. “Generic Bifurcation of Hamiltonian Vector Fields with
Symmetry.” Nonlinearity, 1992, pp. 979–96, doi:10.1088/0951-7715/5/4/008.
short: M. Dellnitz, I. Melbourne, J.E. Marsden, Nonlinearity (1992) 979–996.
date_created: 2020-04-15T08:59:25Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1088/0951-7715/5/4/008
language:
- iso: eng
page: 979-996
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Generic bifurcation of Hamiltonian vector fields with symmetry
type: journal_article
user_id: '15701'
year: '1992'
...
---
_id: '16547'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Jerrold E.
full_name: Marsden, Jerrold E.
last_name: Marsden
- first_name: Ian
full_name: Melbourne, Ian
last_name: Melbourne
- first_name: Jürgen
full_name: Scheurle, Jürgen
last_name: Scheurle
citation:
ama: 'Dellnitz M, Marsden JE, Melbourne I, Scheurle J. Generic Bifurcations of Pendula.
In: Bifurcation and Symmetry. Basel; 1992. doi:10.1007/978-3-0348-7536-3_10'
apa: Dellnitz, M., Marsden, J. E., Melbourne, I., & Scheurle, J. (1992). Generic
Bifurcations of Pendula. In Bifurcation and Symmetry. Basel. https://doi.org/10.1007/978-3-0348-7536-3_10
bibtex: '@inbook{Dellnitz_Marsden_Melbourne_Scheurle_1992, place={Basel}, title={Generic
Bifurcations of Pendula}, DOI={10.1007/978-3-0348-7536-3_10},
booktitle={Bifurcation and Symmetry}, author={Dellnitz, Michael and Marsden, Jerrold
E. and Melbourne, Ian and Scheurle, Jürgen}, year={1992} }'
chicago: Dellnitz, Michael, Jerrold E. Marsden, Ian Melbourne, and Jürgen Scheurle.
“Generic Bifurcations of Pendula.” In Bifurcation and Symmetry. Basel,
1992. https://doi.org/10.1007/978-3-0348-7536-3_10.
ieee: M. Dellnitz, J. E. Marsden, I. Melbourne, and J. Scheurle, “Generic Bifurcations
of Pendula,” in Bifurcation and Symmetry, Basel, 1992.
mla: Dellnitz, Michael, et al. “Generic Bifurcations of Pendula.” Bifurcation
and Symmetry, 1992, doi:10.1007/978-3-0348-7536-3_10.
short: 'M. Dellnitz, J.E. Marsden, I. Melbourne, J. Scheurle, in: Bifurcation and
Symmetry, Basel, 1992.'
date_created: 2020-04-15T08:58:01Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-3-0348-7536-3_10
language:
- iso: eng
place: Basel
publication: Bifurcation and Symmetry
publication_identifier:
isbn:
- '9783034875387'
- '9783034875363'
publication_status: published
status: public
title: Generic Bifurcations of Pendula
type: book_chapter
user_id: '15701'
year: '1992'
...
---
_id: '16541'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Ian
full_name: Melbourne, Ian
last_name: Melbourne
citation:
ama: Dellnitz M, Melbourne I. Generic movement of eigenvalues for equivariant self-adjoint
matrices. Journal of Computational and Applied Mathematics. 1994:249-259.
doi:10.1016/0377-0427(94)90032-9
apa: Dellnitz, M., & Melbourne, I. (1994). Generic movement of eigenvalues for
equivariant self-adjoint matrices. Journal of Computational and Applied Mathematics,
249–259. https://doi.org/10.1016/0377-0427(94)90032-9
bibtex: '@article{Dellnitz_Melbourne_1994, title={Generic movement of eigenvalues
for equivariant self-adjoint matrices}, DOI={10.1016/0377-0427(94)90032-9},
journal={Journal of Computational and Applied Mathematics}, author={Dellnitz,
Michael and Melbourne, Ian}, year={1994}, pages={249–259} }'
chicago: Dellnitz, Michael, and Ian Melbourne. “Generic Movement of Eigenvalues
for Equivariant Self-Adjoint Matrices.” Journal of Computational and Applied
Mathematics, 1994, 249–59. https://doi.org/10.1016/0377-0427(94)90032-9.
ieee: M. Dellnitz and I. Melbourne, “Generic movement of eigenvalues for equivariant
self-adjoint matrices,” Journal of Computational and Applied Mathematics,
pp. 249–259, 1994.
mla: Dellnitz, Michael, and Ian Melbourne. “Generic Movement of Eigenvalues for
Equivariant Self-Adjoint Matrices.” Journal of Computational and Applied Mathematics,
1994, pp. 249–59, doi:10.1016/0377-0427(94)90032-9.
short: M. Dellnitz, I. Melbourne, Journal of Computational and Applied Mathematics
(1994) 249–259.
date_created: 2020-04-15T08:44:12Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1016/0377-0427(94)90032-9
language:
- iso: eng
page: 249-259
publication: Journal of Computational and Applied Mathematics
publication_identifier:
issn:
- 0377-0427
publication_status: published
status: public
title: Generic movement of eigenvalues for equivariant self-adjoint matrices
type: journal_article
user_id: '15701'
year: '1994'
...
---
_id: '16612'
author:
- first_name: L.
full_name: Grüne, L.
last_name: Grüne
- first_name: O.
full_name: Junge, O.
last_name: Junge
citation:
ama: Grüne L, Junge O. Global Optimal Control of Perturbed Systems. Journal of
Optimization Theory and Applications. 2007:411-429. doi:10.1007/s10957-007-9312-z
apa: Grüne, L., & Junge, O. (2007). Global Optimal Control of Perturbed Systems.
Journal of Optimization Theory and Applications, 411–429. https://doi.org/10.1007/s10957-007-9312-z
bibtex: '@article{Grüne_Junge_2007, title={Global Optimal Control of Perturbed Systems},
DOI={10.1007/s10957-007-9312-z},
journal={Journal of Optimization Theory and Applications}, author={Grüne, L. and
Junge, O.}, year={2007}, pages={411–429} }'
chicago: Grüne, L., and O. Junge. “Global Optimal Control of Perturbed Systems.”
Journal of Optimization Theory and Applications, 2007, 411–29. https://doi.org/10.1007/s10957-007-9312-z.
ieee: L. Grüne and O. Junge, “Global Optimal Control of Perturbed Systems,” Journal
of Optimization Theory and Applications, pp. 411–429, 2007.
mla: Grüne, L., and O. Junge. “Global Optimal Control of Perturbed Systems.” Journal
of Optimization Theory and Applications, 2007, pp. 411–29, doi:10.1007/s10957-007-9312-z.
short: L. Grüne, O. Junge, Journal of Optimization Theory and Applications (2007)
411–429.
date_created: 2020-04-16T08:03:02Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1007/s10957-007-9312-z
language:
- iso: eng
page: 411-429
publication: Journal of Optimization Theory and Applications
publication_identifier:
issn:
- 0022-3239
- 1573-2878
publication_status: published
status: public
title: Global Optimal Control of Perturbed Systems
type: journal_article
user_id: '15701'
year: '2007'
...
---
_id: '16500'
author:
- first_name: I.
full_name: Chaudhuri, I.
last_name: Chaudhuri
- first_name: S.
full_name: Sertl, S.
last_name: Sertl
- first_name: Z.
full_name: Hajnal, Z.
last_name: Hajnal
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
- first_name: Th.
full_name: Frauenheim, Th.
last_name: Frauenheim
citation:
ama: Chaudhuri I, Sertl S, Hajnal Z, Dellnitz M, Frauenheim T. Global optimization
of silicon nanoclusters. Applied Surface Science. 2004:108-113. doi:10.1016/j.apsusc.2003.11.007
apa: Chaudhuri, I., Sertl, S., Hajnal, Z., Dellnitz, M., & Frauenheim, T. (2004).
Global optimization of silicon nanoclusters. Applied Surface Science, 108–113.
https://doi.org/10.1016/j.apsusc.2003.11.007
bibtex: '@article{Chaudhuri_Sertl_Hajnal_Dellnitz_Frauenheim_2004, title={Global
optimization of silicon nanoclusters}, DOI={10.1016/j.apsusc.2003.11.007},
journal={Applied Surface Science}, author={Chaudhuri, I. and Sertl, S. and Hajnal,
Z. and Dellnitz, M. and Frauenheim, Th.}, year={2004}, pages={108–113} }'
chicago: Chaudhuri, I., S. Sertl, Z. Hajnal, M. Dellnitz, and Th. Frauenheim. “Global
Optimization of Silicon Nanoclusters.” Applied Surface Science, 2004, 108–13.
https://doi.org/10.1016/j.apsusc.2003.11.007.
ieee: I. Chaudhuri, S. Sertl, Z. Hajnal, M. Dellnitz, and T. Frauenheim, “Global
optimization of silicon nanoclusters,” Applied Surface Science, pp. 108–113,
2004.
mla: Chaudhuri, I., et al. “Global Optimization of Silicon Nanoclusters.” Applied
Surface Science, 2004, pp. 108–13, doi:10.1016/j.apsusc.2003.11.007.
short: I. Chaudhuri, S. Sertl, Z. Hajnal, M. Dellnitz, T. Frauenheim, Applied Surface
Science (2004) 108–113.
date_created: 2020-04-14T10:08:09Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1016/j.apsusc.2003.11.007
language:
- iso: eng
page: 108-113
publication: Applied Surface Science
publication_identifier:
issn:
- 0169-4332
publication_status: published
status: public
title: Global optimization of silicon nanoclusters
type: journal_article
user_id: '15701'
year: '2004'
...
---
_id: '16671'
author:
- first_name: Stefan
full_name: Sertl, Stefan
last_name: Sertl
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Sertl S, Dellnitz M. Global Optimization using a Dynamical Systems Approach.
Journal of Global Optimization. 2006:569-587. doi:10.1007/s10898-005-4384-5
apa: Sertl, S., & Dellnitz, M. (2006). Global Optimization using a Dynamical
Systems Approach. Journal of Global Optimization, 569–587. https://doi.org/10.1007/s10898-005-4384-5
bibtex: '@article{Sertl_Dellnitz_2006, title={Global Optimization using a Dynamical
Systems Approach}, DOI={10.1007/s10898-005-4384-5},
journal={Journal of Global Optimization}, author={Sertl, Stefan and Dellnitz,
Michael}, year={2006}, pages={569–587} }'
chicago: Sertl, Stefan, and Michael Dellnitz. “Global Optimization Using a Dynamical
Systems Approach.” Journal of Global Optimization, 2006, 569–87. https://doi.org/10.1007/s10898-005-4384-5.
ieee: S. Sertl and M. Dellnitz, “Global Optimization using a Dynamical Systems Approach,”
Journal of Global Optimization, pp. 569–587, 2006.
mla: Sertl, Stefan, and Michael Dellnitz. “Global Optimization Using a Dynamical
Systems Approach.” Journal of Global Optimization, 2006, pp. 569–87, doi:10.1007/s10898-005-4384-5.
short: S. Sertl, M. Dellnitz, Journal of Global Optimization (2006) 569–587.
date_created: 2020-04-16T10:07:46Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/s10898-005-4384-5
language:
- iso: eng
page: 569-587
publication: Journal of Global Optimization
publication_identifier:
issn:
- 0925-5001
- 1573-2916
publication_status: published
status: public
title: Global Optimization using a Dynamical Systems Approach
type: journal_article
user_id: '15701'
year: '2006'
...
---
_id: '8752'
abstract:
- lang: eng
text: In this article we develop a gradient-based algorithm for the solution of
multiobjective optimization problems with uncertainties. To this end, an additional
condition is derived for the descent direction in order to account for inaccuracies
in the gradients and then incorporated into a subdivision algorithm for the computation
of global solutions to multiobjective optimization problems. Convergence to a
superset of the Pareto set is proved and an upper bound for the maximal distance
to the set of substationary points is given. Besides the applicability to problems
with uncertainties, the algorithm is developed with the intention to use it in
combination with model order reduction techniques in order to efficiently solve
PDE-constrained multiobjective optimization problems.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Peitz S, Dellnitz M. Gradient-Based Multiobjective Optimization with Uncertainties.
In: NEO 2016. Cham; 2017:159-182. doi:10.1007/978-3-319-64063-1_7'
apa: Peitz, S., & Dellnitz, M. (2017). Gradient-Based Multiobjective Optimization
with Uncertainties. In NEO 2016 (pp. 159–182). Cham. https://doi.org/10.1007/978-3-319-64063-1_7
bibtex: '@inproceedings{Peitz_Dellnitz_2017, place={Cham}, title={Gradient-Based
Multiobjective Optimization with Uncertainties}, DOI={10.1007/978-3-319-64063-1_7},
booktitle={NEO 2016}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2017},
pages={159–182} }'
chicago: Peitz, Sebastian, and Michael Dellnitz. “Gradient-Based Multiobjective
Optimization with Uncertainties.” In NEO 2016, 159–82. Cham, 2017. https://doi.org/10.1007/978-3-319-64063-1_7.
ieee: S. Peitz and M. Dellnitz, “Gradient-Based Multiobjective Optimization with
Uncertainties,” in NEO 2016, 2017, pp. 159–182.
mla: Peitz, Sebastian, and Michael Dellnitz. “Gradient-Based Multiobjective Optimization
with Uncertainties.” NEO 2016, 2017, pp. 159–82, doi:10.1007/978-3-319-64063-1_7.
short: 'S. Peitz, M. Dellnitz, in: NEO 2016, Cham, 2017, pp. 159–182.'
date_created: 2019-03-29T13:28:56Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.1007/978-3-319-64063-1_7
language:
- iso: eng
page: 159-182
place: Cham
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: NEO 2016
publication_identifier:
isbn:
- '9783319640624'
- '9783319640631'
issn:
- 1860-949X
- 1860-9503
publication_status: published
status: public
title: Gradient-Based Multiobjective Optimization with Uncertainties
type: conference
user_id: '47427'
year: '2017'
...
---
_id: '16559'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Mirko Hessel-von
full_name: Molo, Mirko Hessel-von
last_name: Molo
- first_name: Philipp
full_name: Metzner, Philipp
last_name: Metzner
- first_name: Robert
full_name: Preis, Robert
last_name: Preis
- first_name: Christof
full_name: Schütte, Christof
last_name: Schütte
citation:
ama: 'Dellnitz M, Molo MH, Metzner P, Preis R, Schütte C. Graph Algorithms for Dynamical
Systems. In: Analysis, Modeling and Simulation of Multiscale Problems.
; 2006. doi:10.1007/3-540-35657-6_23'
apa: Dellnitz, M., Molo, M. H., Metzner, P., Preis, R., & Schütte, C. (2006).
Graph Algorithms for Dynamical Systems. In Analysis, Modeling and Simulation
of Multiscale Problems. https://doi.org/10.1007/3-540-35657-6_23
bibtex: '@inbook{Dellnitz_Molo_Metzner_Preis_Schütte_2006, title={Graph Algorithms
for Dynamical Systems}, DOI={10.1007/3-540-35657-6_23},
booktitle={Analysis, Modeling and Simulation of Multiscale Problems}, author={Dellnitz,
Michael and Molo, Mirko Hessel-von and Metzner, Philipp and Preis, Robert and
Schütte, Christof}, year={2006} }'
chicago: Dellnitz, Michael, Mirko Hessel-von Molo, Philipp Metzner, Robert Preis,
and Christof Schütte. “Graph Algorithms for Dynamical Systems.” In Analysis,
Modeling and Simulation of Multiscale Problems, 2006. https://doi.org/10.1007/3-540-35657-6_23.
ieee: M. Dellnitz, M. H. Molo, P. Metzner, R. Preis, and C. Schütte, “Graph Algorithms
for Dynamical Systems,” in Analysis, Modeling and Simulation of Multiscale
Problems, 2006.
mla: Dellnitz, Michael, et al. “Graph Algorithms for Dynamical Systems.” Analysis,
Modeling and Simulation of Multiscale Problems, 2006, doi:10.1007/3-540-35657-6_23.
short: 'M. Dellnitz, M.H. Molo, P. Metzner, R. Preis, C. Schütte, in: Analysis,
Modeling and Simulation of Multiscale Problems, 2006.'
date_created: 2020-04-15T09:56:14Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/3-540-35657-6_23
publication: Analysis, Modeling and Simulation of Multiscale Problems
publication_identifier:
isbn:
- '9783540356561'
publication_status: published
status: public
title: Graph Algorithms for Dynamical Systems
type: book_chapter
user_id: '15701'
year: '2006'
...
---
_id: '16659'
author:
- first_name: Maik
full_name: Ringkamp, Maik
last_name: Ringkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
citation:
ama: Ringkamp M, Ober-Blöbaum S, Dellnitz M, Schütze O. Handling high-dimensional
problems with multi-objective continuation methods via successive approximation
of the tangent space. Engineering Optimization. 2012:1117-1146. doi:10.1080/0305215x.2011.634407
apa: Ringkamp, M., Ober-Blöbaum, S., Dellnitz, M., & Schütze, O. (2012). Handling
high-dimensional problems with multi-objective continuation methods via successive
approximation of the tangent space. Engineering Optimization, 1117–1146.
https://doi.org/10.1080/0305215x.2011.634407
bibtex: '@article{Ringkamp_Ober-Blöbaum_Dellnitz_Schütze_2012, title={Handling high-dimensional
problems with multi-objective continuation methods via successive approximation
of the tangent space}, DOI={10.1080/0305215x.2011.634407},
journal={Engineering Optimization}, author={Ringkamp, Maik and Ober-Blöbaum, Sina
and Dellnitz, Michael and Schütze, Oliver}, year={2012}, pages={1117–1146} }'
chicago: Ringkamp, Maik, Sina Ober-Blöbaum, Michael Dellnitz, and Oliver Schütze.
“Handling High-Dimensional Problems with Multi-Objective Continuation Methods
via Successive Approximation of the Tangent Space.” Engineering Optimization,
2012, 1117–46. https://doi.org/10.1080/0305215x.2011.634407.
ieee: M. Ringkamp, S. Ober-Blöbaum, M. Dellnitz, and O. Schütze, “Handling high-dimensional
problems with multi-objective continuation methods via successive approximation
of the tangent space,” Engineering Optimization, pp. 1117–1146, 2012.
mla: Ringkamp, Maik, et al. “Handling High-Dimensional Problems with Multi-Objective
Continuation Methods via Successive Approximation of the Tangent Space.” Engineering
Optimization, 2012, pp. 1117–46, doi:10.1080/0305215x.2011.634407.
short: M. Ringkamp, S. Ober-Blöbaum, M. Dellnitz, O. Schütze, Engineering Optimization
(2012) 1117–1146.
date_created: 2020-04-16T09:34:05Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1080/0305215x.2011.634407
language:
- iso: eng
page: 1117-1146
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: Handling high-dimensional problems with multi-objective continuation methods
via successive approximation of the tangent space
type: journal_article
user_id: '15701'
year: '2012'
...
---
_id: '52726'
abstract:
- lang: eng
text: Heteroclinic structures organize global features of dynamical systems. We
analyse whether heteroclinic structures can arise in network dynamics with higher-order
interactions which describe the nonlinear interactions between three or more units.
We find that while commonly analysed model equations such as network dynamics
on undirected hypergraphs may be useful to describe local dynamics such as cluster
synchronization, they give rise to obstructions that allow to design of heteroclinic
structures in phase space. By contrast, directed hypergraphs break the homogeneity
and lead to vector fields that support heteroclinic structures.
article_type: original
author:
- first_name: Christian
full_name: Bick, Christian
last_name: Bick
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
citation:
ama: Bick C, von der Gracht S. Heteroclinic dynamics in network dynamical systems
with higher-order interactions. Journal of Complex Networks. 2024;12(2).
doi:10.1093/comnet/cnae009
apa: Bick, C., & von der Gracht, S. (2024). Heteroclinic dynamics in network
dynamical systems with higher-order interactions. Journal of Complex Networks,
12(2). https://doi.org/10.1093/comnet/cnae009
bibtex: '@article{Bick_von der Gracht_2024, title={Heteroclinic dynamics in network
dynamical systems with higher-order interactions}, volume={12}, DOI={10.1093/comnet/cnae009},
number={2}, journal={Journal of Complex Networks}, publisher={Oxford University
Press (OUP)}, author={Bick, Christian and von der Gracht, Sören}, year={2024}
}'
chicago: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks
12, no. 2 (2024). https://doi.org/10.1093/comnet/cnae009.
ieee: 'C. Bick and S. von der Gracht, “Heteroclinic dynamics in network dynamical
systems with higher-order interactions,” Journal of Complex Networks, vol.
12, no. 2, 2024, doi: 10.1093/comnet/cnae009.'
mla: Bick, Christian, and Sören von der Gracht. “Heteroclinic Dynamics in Network
Dynamical Systems with Higher-Order Interactions.” Journal of Complex Networks,
vol. 12, no. 2, Oxford University Press (OUP), 2024, doi:10.1093/comnet/cnae009.
short: C. Bick, S. von der Gracht, Journal of Complex Networks 12 (2024).
date_created: 2024-03-22T09:04:57Z
date_updated: 2024-03-22T09:11:53Z
ddc:
- '510'
department:
- _id: '101'
doi: 10.1093/comnet/cnae009
external_id:
arxiv:
- '2309.02006'
file:
- access_level: closed
content_type: application/pdf
creator: svdg
date_created: 2024-03-22T09:06:07Z
date_updated: 2024-03-22T09:06:07Z
file_id: '52728'
file_name: heteroclinic-dynamics-in-network-dynamical-systems-with-higher-order-interactions.pdf
file_size: 649155
relation: main_file
success: 1
file_date_updated: 2024-03-22T09:06:07Z
has_accepted_license: '1'
intvolume: ' 12'
issue: '2'
keyword:
- Applied Mathematics
- Computational Mathematics
- Control and Optimization
- Management Science and Operations Research
- Computer Networks and Communications
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://academic.oup.com/comnet/article-pdf/12/2/cnae009/56832119/cnae009.pdf
oa: '1'
publication: Journal of Complex Networks
publication_identifier:
issn:
- 2051-1329
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: Heteroclinic dynamics in network dynamical systems with higher-order interactions
type: journal_article
user_id: '97359'
volume: 12
year: '2024'
...
---
_id: '17041'
author:
- first_name: Cédric M.
full_name: Campos, Cédric M.
last_name: Campos
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Emmanuel
full_name: Trélat, Emmanuel
last_name: Trélat
citation:
ama: Campos CM, Ober-Blöbaum S, Trélat E. High order variational integrators in
the optimal control of mechanical systems. Discrete & Continuous Dynamical
Systems - A. 2015;35(9):4193-4223. doi:10.3934/dcds.2015.35.4193
apa: Campos, C. M., Ober-Blöbaum, S., & Trélat, E. (2015). High order variational
integrators in the optimal control of mechanical systems. Discrete & Continuous
Dynamical Systems - A, 35(9), 4193–4223. https://doi.org/10.3934/dcds.2015.35.4193
bibtex: '@article{Campos_Ober-Blöbaum_Trélat_2015, title={High order variational
integrators in the optimal control of mechanical systems}, volume={35}, DOI={10.3934/dcds.2015.35.4193},
number={9}, journal={Discrete & Continuous Dynamical Systems - A}, author={Campos,
Cédric M. and Ober-Blöbaum, Sina and Trélat, Emmanuel}, year={2015}, pages={4193–4223}
}'
chicago: 'Campos, Cédric M., Sina Ober-Blöbaum, and Emmanuel Trélat. “High Order
Variational Integrators in the Optimal Control of Mechanical Systems.” Discrete
& Continuous Dynamical Systems - A 35, no. 9 (2015): 4193–4223. https://doi.org/10.3934/dcds.2015.35.4193.'
ieee: C. M. Campos, S. Ober-Blöbaum, and E. Trélat, “High order variational integrators
in the optimal control of mechanical systems,” Discrete & Continuous Dynamical
Systems - A, vol. 35, no. 9, pp. 4193–4223, 2015.
mla: Campos, Cédric M., et al. “High Order Variational Integrators in the Optimal
Control of Mechanical Systems.” Discrete & Continuous Dynamical Systems
- A, vol. 35, no. 9, 2015, pp. 4193–223, doi:10.3934/dcds.2015.35.4193.
short: C.M. Campos, S. Ober-Blöbaum, E. Trélat, Discrete & Continuous Dynamical
Systems - A 35 (2015) 4193–4223.
date_created: 2020-05-20T08:21:03Z
date_updated: 2022-01-06T06:53:03Z
department:
- _id: '101'
doi: 10.3934/dcds.2015.35.4193
intvolume: ' 35'
issue: '9'
language:
- iso: eng
page: 4193-4223
publication: Discrete & Continuous Dynamical Systems - A
status: public
title: High order variational integrators in the optimal control of mechanical systems
type: journal_article
user_id: '47427'
volume: 35
year: '2015'
...
---
_id: '49371'
abstract:
- lang: eng
text: "To model dynamical systems on networks with higher order (non-pairwise)\r\ninteractions,
we recently introduced a new class of ODEs on hypernetworks. Here\r\nwe consider
one-parameter synchrony breaking bifurcations in such ODEs. We call\r\na synchrony
breaking steady state branch \"reluctant\" if it is tangent to a\r\nsynchrony
space, but does not lie inside it. We prove that reluctant synchrony\r\nbreaking
is ubiquitous in hypernetwork systems, by constructing a large class\r\nof examples
that support it. We also give an explicit formula for the order of\r\ntangency
to the synchrony space of a reluctant steady state branch."
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
citation:
ama: von der Gracht S, Nijholt E, Rink B. Higher order interactions lead to “reluctant”
synchrony breaking. arXiv:231117186. Published online 2023.
apa: von der Gracht, S., Nijholt, E., & Rink, B. (2023). Higher order interactions
lead to “reluctant” synchrony breaking. In arXiv:2311.17186.
bibtex: '@article{von der Gracht_Nijholt_Rink_2023, title={Higher order interactions
lead to “reluctant” synchrony breaking}, journal={arXiv:2311.17186}, author={von
der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2023} }'
chicago: Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher Order Interactions
Lead to ‘Reluctant’ Synchrony Breaking.” ArXiv:2311.17186, 2023.
ieee: S. von der Gracht, E. Nijholt, and B. Rink, “Higher order interactions lead
to ‘reluctant’ synchrony breaking,” arXiv:2311.17186. 2023.
mla: von der Gracht, Sören, et al. “Higher Order Interactions Lead to ‘Reluctant’
Synchrony Breaking.” ArXiv:2311.17186, 2023.
short: S. von der Gracht, E. Nijholt, B. Rink, ArXiv:2311.17186 (2023).
date_created: 2023-12-01T06:35:29Z
date_updated: 2023-12-01T06:38:44Z
department:
- _id: '101'
external_id:
arxiv:
- '2311.17186'
language:
- iso: eng
publication: arXiv:2311.17186
status: public
title: Higher order interactions lead to "reluctant" synchrony breaking
type: preprint
user_id: '97359'
year: '2023'
...
---
_id: '16667'
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Carlos A.
full_name: Coello Coello, Carlos A.
last_name: Coello Coello
- first_name: Sanaz
full_name: Mostaghim, Sanaz
last_name: Mostaghim
- first_name: El-Ghazali
full_name: Talbi, El-Ghazali
last_name: Talbi
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Schütze O, Coello Coello CA, Mostaghim S, Talbi E-G, Dellnitz M. Hybridizing
evolutionary strategies with continuation methods for solving multi-objective
problems. Engineering Optimization. 2008:383-402. doi:10.1080/03052150701821328
apa: Schütze, O., Coello Coello, C. A., Mostaghim, S., Talbi, E.-G., & Dellnitz,
M. (2008). Hybridizing evolutionary strategies with continuation methods for solving
multi-objective problems. Engineering Optimization, 383–402. https://doi.org/10.1080/03052150701821328
bibtex: '@article{Schütze_Coello Coello_Mostaghim_Talbi_Dellnitz_2008, title={Hybridizing
evolutionary strategies with continuation methods for solving multi-objective
problems}, DOI={10.1080/03052150701821328},
journal={Engineering Optimization}, author={Schütze, Oliver and Coello Coello,
Carlos A. and Mostaghim, Sanaz and Talbi, El-Ghazali and Dellnitz, Michael}, year={2008},
pages={383–402} }'
chicago: Schütze, Oliver, Carlos A. Coello Coello, Sanaz Mostaghim, El-Ghazali Talbi,
and Michael Dellnitz. “Hybridizing Evolutionary Strategies with Continuation Methods
for Solving Multi-Objective Problems.” Engineering Optimization, 2008,
383–402. https://doi.org/10.1080/03052150701821328.
ieee: O. Schütze, C. A. Coello Coello, S. Mostaghim, E.-G. Talbi, and M. Dellnitz,
“Hybridizing evolutionary strategies with continuation methods for solving multi-objective
problems,” Engineering Optimization, pp. 383–402, 2008.
mla: Schütze, Oliver, et al. “Hybridizing Evolutionary Strategies with Continuation
Methods for Solving Multi-Objective Problems.” Engineering Optimization,
2008, pp. 383–402, doi:10.1080/03052150701821328.
short: O. Schütze, C.A. Coello Coello, S. Mostaghim, E.-G. Talbi, M. Dellnitz, Engineering
Optimization (2008) 383–402.
date_created: 2020-04-16T10:01:07Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1080/03052150701821328
language:
- iso: eng
page: 383-402
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: Hybridizing evolutionary strategies with continuation methods for solving multi-objective
problems
type: journal_article
user_id: '15701'
year: '2008'
...
---
_id: '49326'
abstract:
- lang: eng
text: Many networked systems are governed by non-pairwise interactions between nodes.
The resulting higher-order interaction structure can then be encoded by means
of a hypernetwork. In this paper we consider dynamical systems on hypernetworks
by defining a class of admissible maps for every such hypernetwork. We explain
how to classify robust cluster synchronization patterns on hypernetworks by finding
balanced partitions, and we generalize the concept of a graph fibration to the
hypernetwork context. We also show that robust synchronization patterns are only
fully determined by polynomial admissible maps of high order. This means that,
unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order,
i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork,
for the degree of the polynomial admissible maps that determine robust synchronization
patterns. We also demonstrate that this degree is optimal by investigating a class
of examples. We conclude by demonstrating how this effect may cause remarkable
synchrony breaking bifurcations that occur at high polynomial degree.
author:
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Eddie
full_name: Nijholt, Eddie
last_name: Nijholt
- first_name: Bob
full_name: Rink, Bob
last_name: Rink
citation:
ama: 'von der Gracht S, Nijholt E, Rink B. Hypernetworks: Cluster Synchronization
Is a Higher-Order Effect. SIAM Journal on Applied Mathematics. 2023;83(6):2329-2353.
doi:10.1137/23m1561075'
apa: 'von der Gracht, S., Nijholt, E., & Rink, B. (2023). Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect. SIAM Journal on Applied Mathematics,
83(6), 2329–2353. https://doi.org/10.1137/23m1561075'
bibtex: '@article{von der Gracht_Nijholt_Rink_2023, title={Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect}, volume={83}, DOI={10.1137/23m1561075},
number={6}, journal={SIAM Journal on Applied Mathematics}, publisher={Society
for Industrial & Applied Mathematics (SIAM)}, author={von der Gracht, Sören
and Nijholt, Eddie and Rink, Bob}, year={2023}, pages={2329–2353} }'
chicago: 'Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Hypernetworks: Cluster
Synchronization Is a Higher-Order Effect.” SIAM Journal on Applied Mathematics
83, no. 6 (2023): 2329–53. https://doi.org/10.1137/23m1561075.'
ieee: 'S. von der Gracht, E. Nijholt, and B. Rink, “Hypernetworks: Cluster Synchronization
Is a Higher-Order Effect,” SIAM Journal on Applied Mathematics, vol. 83,
no. 6, pp. 2329–2353, 2023, doi: 10.1137/23m1561075.'
mla: 'von der Gracht, Sören, et al. “Hypernetworks: Cluster Synchronization Is a
Higher-Order Effect.” SIAM Journal on Applied Mathematics, vol. 83, no.
6, Society for Industrial & Applied Mathematics (SIAM), 2023, pp. 2329–53,
doi:10.1137/23m1561075.'
short: S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics
83 (2023) 2329–2353.
date_created: 2023-11-29T10:50:05Z
date_updated: 2023-11-29T10:52:23Z
department:
- _id: '101'
doi: 10.1137/23m1561075
external_id:
arxiv:
- '2302.08974'
intvolume: ' 83'
issue: '6'
keyword:
- Applied Mathematics
language:
- iso: eng
page: 2329-2353
publication: SIAM Journal on Applied Mathematics
publication_identifier:
issn:
- 0036-1399
- 1095-712X
publication_status: published
publisher: Society for Industrial & Applied Mathematics (SIAM)
status: public
title: 'Hypernetworks: Cluster Synchronization Is a Higher-Order Effect'
type: journal_article
user_id: '97359'
volume: 83
year: '2023'
...
---
_id: '16713'
author:
- first_name: Christian
full_name: Gölz, Christian
last_name: Gölz
- first_name: Claudia
full_name: Voelcker-Rehage, Claudia
last_name: Voelcker-Rehage
- first_name: Karin
full_name: Mora, Karin
last_name: Mora
- first_name: Eva-Maria
full_name: Reuter, Eva-Maria
last_name: Reuter
- first_name: Ben
full_name: Godde, Ben
last_name: Godde
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Claus
full_name: Reinsberger, Claus
last_name: Reinsberger
- first_name: Solveig
full_name: Vieluf, Solveig
last_name: Vieluf
citation:
ama: Gölz C, Voelcker-Rehage C, Mora K, et al. Improved Neural Control of Movements
Manifests in Expertise-Related Differences in Force Output and Brain Network Dynamics.
Frontiers in Physiology. 2018. doi:10.3389/fphys.2018.01540
apa: Gölz, C., Voelcker-Rehage, C., Mora, K., Reuter, E.-M., Godde, B., Dellnitz,
M., … Vieluf, S. (2018). Improved Neural Control of Movements Manifests in Expertise-Related
Differences in Force Output and Brain Network Dynamics. Frontiers in Physiology.
https://doi.org/10.3389/fphys.2018.01540
bibtex: '@article{Gölz_Voelcker-Rehage_Mora_Reuter_Godde_Dellnitz_Reinsberger_Vieluf_2018,
title={Improved Neural Control of Movements Manifests in Expertise-Related Differences
in Force Output and Brain Network Dynamics}, DOI={10.3389/fphys.2018.01540},
journal={Frontiers in Physiology}, author={Gölz, Christian and Voelcker-Rehage,
Claudia and Mora, Karin and Reuter, Eva-Maria and Godde, Ben and Dellnitz, Michael
and Reinsberger, Claus and Vieluf, Solveig}, year={2018} }'
chicago: Gölz, Christian, Claudia Voelcker-Rehage, Karin Mora, Eva-Maria Reuter,
Ben Godde, Michael Dellnitz, Claus Reinsberger, and Solveig Vieluf. “Improved
Neural Control of Movements Manifests in Expertise-Related Differences in Force
Output and Brain Network Dynamics.” Frontiers in Physiology, 2018. https://doi.org/10.3389/fphys.2018.01540.
ieee: C. Gölz et al., “Improved Neural Control of Movements Manifests in
Expertise-Related Differences in Force Output and Brain Network Dynamics,” Frontiers
in Physiology, 2018.
mla: Gölz, Christian, et al. “Improved Neural Control of Movements Manifests in
Expertise-Related Differences in Force Output and Brain Network Dynamics.” Frontiers
in Physiology, 2018, doi:10.3389/fphys.2018.01540.
short: C. Gölz, C. Voelcker-Rehage, K. Mora, E.-M. Reuter, B. Godde, M. Dellnitz,
C. Reinsberger, S. Vieluf, Frontiers in Physiology (2018).
date_created: 2020-04-16T14:08:06Z
date_updated: 2022-01-06T06:52:55Z
department:
- _id: '101'
doi: 10.3389/fphys.2018.01540
language:
- iso: eng
publication: Frontiers in Physiology
publication_identifier:
issn:
- 1664-042X
publication_status: published
status: public
title: Improved Neural Control of Movements Manifests in Expertise-Related Differences
in Force Output and Brain Network Dynamics
type: journal_article
user_id: '47427'
year: '2018'
...
---
_id: '16696'
author:
- first_name: A.
full_name: Zanzottera, A.
last_name: Zanzottera
- first_name: G.
full_name: Mingotti, G.
last_name: Mingotti
- first_name: R.
full_name: Castelli, R.
last_name: Castelli
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
citation:
ama: 'Zanzottera A, Mingotti G, Castelli R, Dellnitz M. Intersecting invariant manifolds
in spatial restricted three-body problems: Design and optimization of Earth-to-halo
transfers in the Sun–Earth–Moon scenario. Communications in Nonlinear Science
and Numerical Simulation. 2012:832-843. doi:10.1016/j.cnsns.2011.06.032'
apa: 'Zanzottera, A., Mingotti, G., Castelli, R., & Dellnitz, M. (2012). Intersecting
invariant manifolds in spatial restricted three-body problems: Design and optimization
of Earth-to-halo transfers in the Sun–Earth–Moon scenario. Communications in
Nonlinear Science and Numerical Simulation, 832–843. https://doi.org/10.1016/j.cnsns.2011.06.032'
bibtex: '@article{Zanzottera_Mingotti_Castelli_Dellnitz_2012, title={Intersecting
invariant manifolds in spatial restricted three-body problems: Design and optimization
of Earth-to-halo transfers in the Sun–Earth–Moon scenario}, DOI={10.1016/j.cnsns.2011.06.032},
journal={Communications in Nonlinear Science and Numerical Simulation}, author={Zanzottera,
A. and Mingotti, G. and Castelli, R. and Dellnitz, M.}, year={2012}, pages={832–843}
}'
chicago: 'Zanzottera, A., G. Mingotti, R. Castelli, and M. Dellnitz. “Intersecting
Invariant Manifolds in Spatial Restricted Three-Body Problems: Design and Optimization
of Earth-to-Halo Transfers in the Sun–Earth–Moon Scenario.” Communications
in Nonlinear Science and Numerical Simulation, 2012, 832–43. https://doi.org/10.1016/j.cnsns.2011.06.032.'
ieee: 'A. Zanzottera, G. Mingotti, R. Castelli, and M. Dellnitz, “Intersecting invariant
manifolds in spatial restricted three-body problems: Design and optimization of
Earth-to-halo transfers in the Sun–Earth–Moon scenario,” Communications in
Nonlinear Science and Numerical Simulation, pp. 832–843, 2012.'
mla: 'Zanzottera, A., et al. “Intersecting Invariant Manifolds in Spatial Restricted
Three-Body Problems: Design and Optimization of Earth-to-Halo Transfers in the
Sun–Earth–Moon Scenario.” Communications in Nonlinear Science and Numerical
Simulation, 2012, pp. 832–43, doi:10.1016/j.cnsns.2011.06.032.'
short: A. Zanzottera, G. Mingotti, R. Castelli, M. Dellnitz, Communications in Nonlinear
Science and Numerical Simulation (2012) 832–843.
date_created: 2020-04-16T10:56:56Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1016/j.cnsns.2011.06.032
language:
- iso: eng
page: 832-843
publication: Communications in Nonlinear Science and Numerical Simulation
publication_identifier:
issn:
- 1007-5704
publication_status: published
status: public
title: 'Intersecting invariant manifolds in spatial restricted three-body problems:
Design and optimization of Earth-to-halo transfers in the Sun–Earth–Moon scenario'
type: journal_article
user_id: '15701'
year: '2012'
...
---
_id: '16295'
abstract:
- lang: eng
text: It is a challenging task to identify the objectives on which a certain decision
was based, in particular if several, potentially conflicting criteria are equally
important and a continuous set of optimal compromise decisions exists. This task
can be understood as the inverse problem of multiobjective optimization, where
the goal is to find the objective function vector of a given Pareto set. To this
end, we present a method to construct the objective function vector of an unconstrained
multiobjective optimization problem (MOP) such that the Pareto critical set contains
a given set of data points with prescribed KKT multipliers. If such an MOP can
not be found, then the method instead produces an MOP whose Pareto critical set
is at least close to the data points. The key idea is to consider the objective
function vector in the multiobjective KKT conditions as variable and then search
for the objectives that minimize the Euclidean norm of the resulting system of
equations. By expressing the objectives in a finite-dimensional basis, we transform
this problem into a homogeneous, linear system of equations that can be solved
efficiently. Potential applications of this approach include the identification
of objectives (both from clean and noisy data) and the construction of surrogate
models for expensive MOPs.
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: 'Gebken B, Peitz S. Inverse multiobjective optimization: Inferring decision
criteria from data. Journal of Global Optimization. 2021;80:3-29. doi:10.1007/s10898-020-00983-z'
apa: 'Gebken, B., & Peitz, S. (2021). Inverse multiobjective optimization: Inferring
decision criteria from data. Journal of Global Optimization, 80,
3–29. https://doi.org/10.1007/s10898-020-00983-z'
bibtex: '@article{Gebken_Peitz_2021, title={Inverse multiobjective optimization:
Inferring decision criteria from data}, volume={80}, DOI={10.1007/s10898-020-00983-z},
journal={Journal of Global Optimization}, publisher={Springer}, author={Gebken,
Bennet and Peitz, Sebastian}, year={2021}, pages={3–29} }'
chicago: 'Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization:
Inferring Decision Criteria from Data.” Journal of Global Optimization
80 (2021): 3–29. https://doi.org/10.1007/s10898-020-00983-z.'
ieee: 'B. Gebken and S. Peitz, “Inverse multiobjective optimization: Inferring decision
criteria from data,” Journal of Global Optimization, vol. 80, pp. 3–29,
2021.'
mla: 'Gebken, Bennet, and Sebastian Peitz. “Inverse Multiobjective Optimization:
Inferring Decision Criteria from Data.” Journal of Global Optimization,
vol. 80, Springer, 2021, pp. 3–29, doi:10.1007/s10898-020-00983-z.'
short: B. Gebken, S. Peitz, Journal of Global Optimization 80 (2021) 3–29.
date_created: 2020-03-13T12:45:05Z
date_updated: 2022-01-06T06:52:48Z
department:
- _id: '101'
doi: 10.1007/s10898-020-00983-z
intvolume: ' 80'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10898-020-00983-z.pdf
oa: '1'
page: 3-29
publication: Journal of Global Optimization
publisher: Springer
status: public
title: 'Inverse multiobjective optimization: Inferring decision criteria from data'
type: journal_article
user_id: '47427'
volume: 80
year: '2021'
...
---
_id: '21819'
abstract:
- lang: eng
text: Many dimensionality and model reduction techniques rely on estimating
dominant eigenfunctions of associated dynamical operators from data. Important
examples include the Koopman operator and its generator, but also the Schrödinger
operator. We propose a kernel-based method for the approximation of differential
operators in reproducing kernel Hilbert spaces and show how eigenfunctions can
be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms
are applied to molecular dynamics and quantum chemistry examples. Furthermore,
we exploit that, under certain conditions, the Schrödinger operator can be transformed
into a Kolmogorov backward operator corresponding to a drift-diffusion process
and vice versa. This allows us to apply methods developed for the analysis of
high-dimensional stochastic differential equations to quantum mechanical systems.
article_number: '722'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Boumediene
full_name: Hamzi, Boumediene
last_name: Hamzi
citation:
ama: Klus S, Nüske F, Hamzi B. Kernel-Based Approximation of the Koopman Generator
and Schrödinger Operator. Entropy. 2020. doi:10.3390/e22070722
apa: Klus, S., Nüske, F., & Hamzi, B. (2020). Kernel-Based Approximation of
the Koopman Generator and Schrödinger Operator. Entropy. https://doi.org/10.3390/e22070722
bibtex: '@article{Klus_Nüske_Hamzi_2020, title={Kernel-Based Approximation of the
Koopman Generator and Schrödinger Operator}, DOI={10.3390/e22070722},
number={722}, journal={Entropy}, author={Klus, Stefan and Nüske, Feliks and Hamzi,
Boumediene}, year={2020} }'
chicago: Klus, Stefan, Feliks Nüske, and Boumediene Hamzi. “Kernel-Based Approximation
of the Koopman Generator and Schrödinger Operator.” Entropy, 2020. https://doi.org/10.3390/e22070722.
ieee: S. Klus, F. Nüske, and B. Hamzi, “Kernel-Based Approximation of the Koopman
Generator and Schrödinger Operator,” Entropy, 2020.
mla: Klus, Stefan, et al. “Kernel-Based Approximation of the Koopman Generator and
Schrödinger Operator.” Entropy, 722, 2020, doi:10.3390/e22070722.
short: S. Klus, F. Nüske, B. Hamzi, Entropy (2020).
date_created: 2021-04-28T18:06:35Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e22070722
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/1099-4300/22/7/722
oa: '1'
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
status: public
title: Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator
type: journal_article
user_id: '81513'
year: '2020'
...
---
_id: '29673'
abstract:
- lang: eng
text: Koopman operator theory has been successfully applied to problems from various
research areas such as fluid dynamics, molecular dynamics, climate science, engineering,
and biology. Applications include detecting metastable or coherent sets, coarse-graining,
system identification, and control. There is an intricate connection between dynamical
systems driven by stochastic differential equations and quantum mechanics. In
this paper, we compare the ground-state transformation and Nelson's stochastic
mechanics and demonstrate how data-driven methods developed for the approximation
of the Koopman operator can be used to analyze quantum physics problems. Moreover,
we exploit the relationship between Schrödinger operators and stochastic control
problems to show that modern data-driven methods for stochastic control can be
used to solve the stationary or imaginary-time Schrödinger equation. Our findings
open up a new avenue towards solving Schrödinger's equation using recently developed
tools from data science.
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Klus S, Nüske F, Peitz S. Koopman analysis of quantum systems. Journal
of Physics A: Mathematical and Theoretical. 2022;55(31):314002. doi:10.1088/1751-8121/ac7d22'
apa: 'Klus, S., Nüske, F., & Peitz, S. (2022). Koopman analysis of quantum systems.
Journal of Physics A: Mathematical and Theoretical, 55(31), 314002.
https://doi.org/10.1088/1751-8121/ac7d22'
bibtex: '@article{Klus_Nüske_Peitz_2022, title={Koopman analysis of quantum systems},
volume={55}, DOI={10.1088/1751-8121/ac7d22},
number={31}, journal={Journal of Physics A: Mathematical and Theoretical}, publisher={IOP
Publishing Ltd.}, author={Klus, Stefan and Nüske, Feliks and Peitz, Sebastian},
year={2022}, pages={314002} }'
chicago: 'Klus, Stefan, Feliks Nüske, and Sebastian Peitz. “Koopman Analysis of
Quantum Systems.” Journal of Physics A: Mathematical and Theoretical 55,
no. 31 (2022): 314002. https://doi.org/10.1088/1751-8121/ac7d22.'
ieee: 'S. Klus, F. Nüske, and S. Peitz, “Koopman analysis of quantum systems,” Journal
of Physics A: Mathematical and Theoretical, vol. 55, no. 31, p. 314002, 2022,
doi: 10.1088/1751-8121/ac7d22.'
mla: 'Klus, Stefan, et al. “Koopman Analysis of Quantum Systems.” Journal of
Physics A: Mathematical and Theoretical, vol. 55, no. 31, IOP Publishing Ltd.,
2022, p. 314002, doi:10.1088/1751-8121/ac7d22.'
short: 'S. Klus, F. Nüske, S. Peitz, Journal of Physics A: Mathematical and Theoretical
55 (2022) 314002.'
date_created: 2022-01-31T09:49:40Z
date_updated: 2022-07-18T14:26:41Z
department:
- _id: '655'
- _id: '101'
doi: 10.1088/1751-8121/ac7d22
external_id:
arxiv:
- '2201.12062'
intvolume: ' 55'
issue: '31'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://iopscience.iop.org/article/10.1088/1751-8121/ac7d22/pdf
oa: '1'
page: '314002'
publication: 'Journal of Physics A: Mathematical and Theoretical'
publication_status: published
publisher: IOP Publishing Ltd.
status: public
title: Koopman analysis of quantum systems
type: journal_article
user_id: '47427'
volume: 55
year: '2022'
...
---
_id: '21634'
abstract:
- lang: eng
text: "Predictive control of power electronic systems always requires a suitable\r\nmodel
of the plant. Using typical physics-based white box models, a trade-off\r\nbetween
model complexity (i.e. accuracy) and computational burden has to be\r\nmade. This
is a challenging task with a lot of constraints, since the model\r\norder is directly
linked to the number of system states. Even though white-box\r\nmodels show suitable
performance in most cases, parasitic real-world effects\r\noften cannot be modeled
satisfactorily with an expedient computational load.\r\nHence, a Koopman operator-based
model reduction technique is presented which\r\ndirectly links the control action
to the system's outputs in a black-box\r\nfashion. The Koopman operator is a linear
but infinite-dimensional operator\r\ndescribing the dynamics of observables of
nonlinear autonomous dynamical\r\nsystems which can be nicely applied to the switching
principle of power\r\nelectronic devices. Following this data-driven approach,
the model order and\r\nthe number of system states are decoupled which allows
us to consider more\r\ncomplex systems. Extensive experimental tests with an automotive-type
permanent\r\nmagnet synchronous motor fed by an IGBT 2-level inverter prove the
feasibility\r\nof the proposed modeling technique in a finite-set model predictive
control\r\napplication."
author:
- first_name: Sören
full_name: Hanke, Sören
last_name: Hanke
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Oliver
full_name: Wallscheid, Oliver
last_name: Wallscheid
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Joachim
full_name: Böcker, Joachim
last_name: Böcker
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Hanke S, Peitz S, Wallscheid O, Klus S, Böcker J, Dellnitz M. Koopman Operator-Based
Finite-Control-Set Model Predictive Control for Electrical Drives. arXiv:180400854.
2018.
apa: Hanke, S., Peitz, S., Wallscheid, O., Klus, S., Böcker, J., & Dellnitz,
M. (2018). Koopman Operator-Based Finite-Control-Set Model Predictive Control
for Electrical Drives. ArXiv:1804.00854.
bibtex: '@article{Hanke_Peitz_Wallscheid_Klus_Böcker_Dellnitz_2018, title={Koopman
Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives},
journal={arXiv:1804.00854}, author={Hanke, Sören and Peitz, Sebastian and Wallscheid,
Oliver and Klus, Stefan and Böcker, Joachim and Dellnitz, Michael}, year={2018}
}'
chicago: Hanke, Sören, Sebastian Peitz, Oliver Wallscheid, Stefan Klus, Joachim
Böcker, and Michael Dellnitz. “Koopman Operator-Based Finite-Control-Set Model
Predictive Control for Electrical Drives.” ArXiv:1804.00854, 2018.
ieee: S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, and M. Dellnitz, “Koopman
Operator-Based Finite-Control-Set Model Predictive Control for Electrical Drives,”
arXiv:1804.00854. 2018.
mla: Hanke, Sören, et al. “Koopman Operator-Based Finite-Control-Set Model Predictive
Control for Electrical Drives.” ArXiv:1804.00854, 2018.
short: S. Hanke, S. Peitz, O. Wallscheid, S. Klus, J. Böcker, M. Dellnitz, ArXiv:1804.00854
(2018).
date_created: 2021-04-19T16:17:30Z
date_updated: 2022-01-06T06:55:08Z
department:
- _id: '101'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/1804.00854.pdf
oa: '1'
publication: arXiv:1804.00854
status: public
title: Koopman Operator-Based Finite-Control-Set Model Predictive Control for Electrical
Drives
type: preprint
user_id: '47427'
year: '2018'
...
---
_id: '10593'
abstract:
- lang: eng
text: We present a new framework for optimal and feedback control of PDEs using
Koopman operator-based reduced order models (K-ROMs). The Koopman operator is
a linear but infinite-dimensional operator which describes the dynamics of observables.
A numerical approximation of the Koopman operator therefore yields a linear system
for the observation of an autonomous dynamical system. In our approach, by introducing
a finite number of constant controls, the dynamic control system is transformed
into a set of autonomous systems and the corresponding optimal control problem
into a switching time optimization problem. This allows us to replace each of
these systems by a K-ROM which can be solved orders of magnitude faster. By this
approach, a nonlinear infinite-dimensional control problem is transformed into
a low-dimensional linear problem. Using a recent convergence result for the numerical
approximation via Extended Dynamic Mode Decomposition (EDMD), we show that the
value of the K-ROM based objective function converges in measure to the value
of the full objective function. To illustrate the results, we consider the 1D
Burgers equation and the 2D Navier–Stokes equations. The numerical experiments
show remarkable performance concerning both solution times and accuracy.
article_type: original
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
citation:
ama: Peitz S, Klus S. Koopman operator-based model reduction for switched-system
control of PDEs. Automatica. 2019;106:184-191. doi:10.1016/j.automatica.2019.05.016
apa: Peitz, S., & Klus, S. (2019). Koopman operator-based model reduction for
switched-system control of PDEs. Automatica, 106, 184–191. https://doi.org/10.1016/j.automatica.2019.05.016
bibtex: '@article{Peitz_Klus_2019, title={Koopman operator-based model reduction
for switched-system control of PDEs}, volume={106}, DOI={10.1016/j.automatica.2019.05.016},
journal={Automatica}, author={Peitz, Sebastian and Klus, Stefan}, year={2019},
pages={184–191} }'
chicago: 'Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction
for Switched-System Control of PDEs.” Automatica 106 (2019): 184–91. https://doi.org/10.1016/j.automatica.2019.05.016.'
ieee: S. Peitz and S. Klus, “Koopman operator-based model reduction for switched-system
control of PDEs,” Automatica, vol. 106, pp. 184–191, 2019.
mla: Peitz, Sebastian, and Stefan Klus. “Koopman Operator-Based Model Reduction
for Switched-System Control of PDEs.” Automatica, vol. 106, 2019, pp. 184–91,
doi:10.1016/j.automatica.2019.05.016.
short: S. Peitz, S. Klus, Automatica 106 (2019) 184–191.
date_created: 2019-07-10T08:08:16Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1016/j.automatica.2019.05.016
intvolume: ' 106'
language:
- iso: eng
page: 184-191
publication: Automatica
publication_identifier:
issn:
- 0005-1098
publication_status: published
status: public
title: Koopman operator-based model reduction for switched-system control of PDEs
type: journal_article
user_id: '47427'
volume: 106
year: '2019'
...
---
_id: '16648'
author:
- first_name: Kathrin
full_name: Padberg, Kathrin
last_name: Padberg
- first_name: Thilo
full_name: Hauff, Thilo
last_name: Hauff
- first_name: Frank
full_name: Jenko, Frank
last_name: Jenko
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: Padberg K, Hauff T, Jenko F, Junge O. Lagrangian structures and transport in
turbulent magnetized plasmas. New Journal of Physics. 2007:400-400. doi:10.1088/1367-2630/9/11/400
apa: Padberg, K., Hauff, T., Jenko, F., & Junge, O. (2007). Lagrangian structures
and transport in turbulent magnetized plasmas. New Journal of Physics,
400–400. https://doi.org/10.1088/1367-2630/9/11/400
bibtex: '@article{Padberg_Hauff_Jenko_Junge_2007, title={Lagrangian structures and
transport in turbulent magnetized plasmas}, DOI={10.1088/1367-2630/9/11/400},
journal={New Journal of Physics}, author={Padberg, Kathrin and Hauff, Thilo and
Jenko, Frank and Junge, Oliver}, year={2007}, pages={400–400} }'
chicago: Padberg, Kathrin, Thilo Hauff, Frank Jenko, and Oliver Junge. “Lagrangian
Structures and Transport in Turbulent Magnetized Plasmas.” New Journal of Physics,
2007, 400–400. https://doi.org/10.1088/1367-2630/9/11/400.
ieee: K. Padberg, T. Hauff, F. Jenko, and O. Junge, “Lagrangian structures and transport
in turbulent magnetized plasmas,” New Journal of Physics, pp. 400–400,
2007.
mla: Padberg, Kathrin, et al. “Lagrangian Structures and Transport in Turbulent
Magnetized Plasmas.” New Journal of Physics, 2007, pp. 400–400, doi:10.1088/1367-2630/9/11/400.
short: K. Padberg, T. Hauff, F. Jenko, O. Junge, New Journal of Physics (2007) 400–400.
date_created: 2020-04-16T09:10:26Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1088/1367-2630/9/11/400
page: 400-400
publication: New Journal of Physics
publication_identifier:
issn:
- 1367-2630
publication_status: published
status: public
title: Lagrangian structures and transport in turbulent magnetized plasmas
type: journal_article
user_id: '15701'
year: '2007'
...
---
_id: '16649'
author:
- first_name: Kathrin
full_name: Padberg, Kathrin
last_name: Padberg
- first_name: Bianca
full_name: Thiere, Bianca
last_name: Thiere
- first_name: Robert
full_name: Preis, Robert
last_name: Preis
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Padberg K, Thiere B, Preis R, Dellnitz M. Local expansion concepts for detecting
transport barriers in dynamical systems. Communications in Nonlinear Science
and Numerical Simulation. 2009:4176-4190. doi:10.1016/j.cnsns.2009.03.018
apa: Padberg, K., Thiere, B., Preis, R., & Dellnitz, M. (2009). Local expansion
concepts for detecting transport barriers in dynamical systems. Communications
in Nonlinear Science and Numerical Simulation, 4176–4190. https://doi.org/10.1016/j.cnsns.2009.03.018
bibtex: '@article{Padberg_Thiere_Preis_Dellnitz_2009, title={Local expansion concepts
for detecting transport barriers in dynamical systems}, DOI={10.1016/j.cnsns.2009.03.018},
journal={Communications in Nonlinear Science and Numerical Simulation}, author={Padberg,
Kathrin and Thiere, Bianca and Preis, Robert and Dellnitz, Michael}, year={2009},
pages={4176–4190} }'
chicago: Padberg, Kathrin, Bianca Thiere, Robert Preis, and Michael Dellnitz. “Local
Expansion Concepts for Detecting Transport Barriers in Dynamical Systems.” Communications
in Nonlinear Science and Numerical Simulation, 2009, 4176–90. https://doi.org/10.1016/j.cnsns.2009.03.018.
ieee: K. Padberg, B. Thiere, R. Preis, and M. Dellnitz, “Local expansion concepts
for detecting transport barriers in dynamical systems,” Communications in Nonlinear
Science and Numerical Simulation, pp. 4176–4190, 2009.
mla: Padberg, Kathrin, et al. “Local Expansion Concepts for Detecting Transport
Barriers in Dynamical Systems.” Communications in Nonlinear Science and Numerical
Simulation, 2009, pp. 4176–90, doi:10.1016/j.cnsns.2009.03.018.
short: K. Padberg, B. Thiere, R. Preis, M. Dellnitz, Communications in Nonlinear
Science and Numerical Simulation (2009) 4176–4190.
date_created: 2020-04-16T09:11:26Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1016/j.cnsns.2009.03.018
language:
- iso: eng
page: 4176-4190
publication: Communications in Nonlinear Science and Numerical Simulation
publication_identifier:
issn:
- 1007-5704
publication_status: published
status: public
title: Local expansion concepts for detecting transport barriers in dynamical systems
type: journal_article
user_id: '15701'
year: '2009'
...
---
_id: '16599'
author:
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
citation:
ama: 'Froyland G. Markov modelling for random dynamical systems. In: Equadiff
99. ; 2013. doi:10.1142/9789812792617_0200'
apa: Froyland, G. (2013). Markov modelling for random dynamical systems. In Equadiff
99. https://doi.org/10.1142/9789812792617_0200
bibtex: '@inbook{Froyland_2013, title={Markov modelling for random dynamical systems},
DOI={10.1142/9789812792617_0200},
booktitle={Equadiff 99}, author={Froyland, Gary}, year={2013} }'
chicago: Froyland, Gary. “Markov Modelling for Random Dynamical Systems.” In Equadiff
99, 2013. https://doi.org/10.1142/9789812792617_0200.
ieee: G. Froyland, “Markov modelling for random dynamical systems,” in Equadiff
99, 2013.
mla: Froyland, Gary. “Markov Modelling for Random Dynamical Systems.” Equadiff
99, 2013, doi:10.1142/9789812792617_0200.
short: 'G. Froyland, in: Equadiff 99, 2013.'
date_created: 2020-04-16T06:05:19Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1142/9789812792617_0200
publication: Equadiff 99
publication_identifier:
isbn:
- '9789810243593'
- '9789812792617'
publication_status: published
status: public
title: Markov modelling for random dynamical systems
type: book_chapter
user_id: '15701'
year: '2013'
...
---
_id: '21938'
article_number: '094104'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Hao
full_name: Wu, Hao
last_name: Wu
- first_name: Jan-Hendrik
full_name: Prinz, Jan-Hendrik
last_name: Prinz
- first_name: Christoph
full_name: Wehmeyer, Christoph
last_name: Wehmeyer
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
- first_name: Frank
full_name: Noé, Frank
last_name: Noé
citation:
ama: Nüske F, Wu H, Prinz J-H, Wehmeyer C, Clementi C, Noé F. Markov state models
from short non-equilibrium simulations—Analysis and correction of estimation bias.
The Journal of Chemical Physics. 2017. doi:10.1063/1.4976518
apa: Nüske, F., Wu, H., Prinz, J.-H., Wehmeyer, C., Clementi, C., & Noé, F.
(2017). Markov state models from short non-equilibrium simulations—Analysis and
correction of estimation bias. The Journal of Chemical Physics. https://doi.org/10.1063/1.4976518
bibtex: '@article{Nüske_Wu_Prinz_Wehmeyer_Clementi_Noé_2017, title={Markov state
models from short non-equilibrium simulations—Analysis and correction of estimation
bias}, DOI={10.1063/1.4976518},
number={094104}, journal={The Journal of Chemical Physics}, author={Nüske, Feliks
and Wu, Hao and Prinz, Jan-Hendrik and Wehmeyer, Christoph and Clementi, Cecilia
and Noé, Frank}, year={2017} }'
chicago: Nüske, Feliks, Hao Wu, Jan-Hendrik Prinz, Christoph Wehmeyer, Cecilia Clementi,
and Frank Noé. “Markov State Models from Short Non-Equilibrium Simulations—Analysis
and Correction of Estimation Bias.” The Journal of Chemical Physics, 2017.
https://doi.org/10.1063/1.4976518.
ieee: F. Nüske, H. Wu, J.-H. Prinz, C. Wehmeyer, C. Clementi, and F. Noé, “Markov
state models from short non-equilibrium simulations—Analysis and correction of
estimation bias,” The Journal of Chemical Physics, 2017.
mla: Nüske, Feliks, et al. “Markov State Models from Short Non-Equilibrium Simulations—Analysis
and Correction of Estimation Bias.” The Journal of Chemical Physics, 094104,
2017, doi:10.1063/1.4976518.
short: F. Nüske, H. Wu, J.-H. Prinz, C. Wehmeyer, C. Clementi, F. Noé, The Journal
of Chemical Physics (2017).
date_created: 2021-04-30T16:55:31Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.4976518
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
issn:
- 0021-9606
- 1089-7690
publication_status: published
status: public
title: Markov state models from short non-equilibrium simulations—Analysis and correction
of estimation bias
type: journal_article
user_id: '81513'
year: '2017'
...
---
_id: '16546'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Martin
full_name: Golubitsky, Martin
last_name: Golubitsky
- first_name: Ian
full_name: Melbourne, Ian
last_name: Melbourne
citation:
ama: 'Dellnitz M, Golubitsky M, Melbourne I. Mechanisms of Symmetry Creation. In:
Bifurcation and Symmetry. Basel; 1992. doi:10.1007/978-3-0348-7536-3_9'
apa: Dellnitz, M., Golubitsky, M., & Melbourne, I. (1992). Mechanisms of Symmetry
Creation. In Bifurcation and Symmetry. Basel. https://doi.org/10.1007/978-3-0348-7536-3_9
bibtex: '@inbook{Dellnitz_Golubitsky_Melbourne_1992, place={Basel}, title={Mechanisms
of Symmetry Creation}, DOI={10.1007/978-3-0348-7536-3_9},
booktitle={Bifurcation and Symmetry}, author={Dellnitz, Michael and Golubitsky,
Martin and Melbourne, Ian}, year={1992} }'
chicago: Dellnitz, Michael, Martin Golubitsky, and Ian Melbourne. “Mechanisms of
Symmetry Creation.” In Bifurcation and Symmetry. Basel, 1992. https://doi.org/10.1007/978-3-0348-7536-3_9.
ieee: M. Dellnitz, M. Golubitsky, and I. Melbourne, “Mechanisms of Symmetry Creation,”
in Bifurcation and Symmetry, Basel, 1992.
mla: Dellnitz, Michael, et al. “Mechanisms of Symmetry Creation.” Bifurcation
and Symmetry, 1992, doi:10.1007/978-3-0348-7536-3_9.
short: 'M. Dellnitz, M. Golubitsky, I. Melbourne, in: Bifurcation and Symmetry,
Basel, 1992.'
date_created: 2020-04-15T08:56:42Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-3-0348-7536-3_9
language:
- iso: eng
place: Basel
publication: Bifurcation and Symmetry
publication_identifier:
isbn:
- '9783034875387'
- '9783034875363'
publication_status: published
status: public
title: Mechanisms of Symmetry Creation
type: book_chapter
user_id: '15701'
year: '1992'
...
---
_id: '16679'
author:
- first_name: Harald
full_name: Anacker, Harald
last_name: Anacker
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Stefan
full_name: Groesbrink, Stefan
last_name: Groesbrink
- first_name: Philip
full_name: Hartmann, Philip
last_name: Hartmann
- first_name: Christian
full_name: Heinzemann, Christian
last_name: Heinzemann
- first_name: Christian
full_name: Horenkamp, Christian
last_name: Horenkamp
- first_name: Bernd
full_name: Kleinjohann, Bernd
last_name: Kleinjohann
- first_name: Lisa
full_name: Kleinjohann, Lisa
last_name: Kleinjohann
- first_name: Sebastian
full_name: Korf, Sebastian
last_name: Korf
- first_name: Martin
full_name: Krüger, Martin
last_name: Krüger
- first_name: Wolfgang
full_name: Müller, Wolfgang
last_name: Müller
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Simon
full_name: Oberthür, Simon
last_name: Oberthür
- first_name: Mario
full_name: Porrmann, Mario
last_name: Porrmann
- first_name: Claudia
full_name: Priesterjahn, Claudia
last_name: Priesterjahn
- first_name: Rafael
full_name: Radkowski, Rafael
last_name: Radkowski
- first_name: Christoph
full_name: Rasche, Christoph
last_name: Rasche
- first_name: Jan
full_name: Rieke, Jan
last_name: Rieke
- first_name: Maik
full_name: Ringkamp, Maik
last_name: Ringkamp
- first_name: Katharina
full_name: Stahl, Katharina
last_name: Stahl
- first_name: Dominik
full_name: Steenken, Dominik
last_name: Steenken
- first_name: Jörg
full_name: Stöcklein, Jörg
last_name: Stöcklein
- first_name: Robert
full_name: Timmermann, Robert
last_name: Timmermann
- first_name: Ansgar
full_name: Trächtler, Ansgar
last_name: Trächtler
- first_name: Katrin
full_name: Witting, Katrin
last_name: Witting
- first_name: Tao
full_name: Xie, Tao
last_name: Xie
- first_name: Steffen
full_name: Ziegert, Steffen
last_name: Ziegert
citation:
ama: 'Anacker H, Dellnitz M, Flaßkamp K, et al. Methods for the Design and Development.
In: Lecture Notes in Mechanical Engineering. Berlin, Heidelberg; 2014.
doi:10.1007/978-3-642-45435-6_5'
apa: Anacker, H., Dellnitz, M., Flaßkamp, K., Groesbrink, S., Hartmann, P., Heinzemann,
C., … Ziegert, S. (2014). Methods for the Design and Development. In Lecture
Notes in Mechanical Engineering. Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45435-6_5
bibtex: '@inbook{Anacker_Dellnitz_Flaßkamp_Groesbrink_Hartmann_Heinzemann_Horenkamp_Kleinjohann_Kleinjohann_Korf_et
al._2014, place={Berlin, Heidelberg}, title={Methods for the Design and Development},
DOI={10.1007/978-3-642-45435-6_5},
booktitle={Lecture Notes in Mechanical Engineering}, author={Anacker, Harald and
Dellnitz, Michael and Flaßkamp, Kathrin and Groesbrink, Stefan and Hartmann, Philip
and Heinzemann, Christian and Horenkamp, Christian and Kleinjohann, Bernd and
Kleinjohann, Lisa and Korf, Sebastian and et al.}, year={2014} }'
chicago: Anacker, Harald, Michael Dellnitz, Kathrin Flaßkamp, Stefan Groesbrink,
Philip Hartmann, Christian Heinzemann, Christian Horenkamp, et al. “Methods for
the Design and Development.” In Lecture Notes in Mechanical Engineering.
Berlin, Heidelberg, 2014. https://doi.org/10.1007/978-3-642-45435-6_5.
ieee: H. Anacker et al., “Methods for the Design and Development,” in Lecture
Notes in Mechanical Engineering, Berlin, Heidelberg, 2014.
mla: Anacker, Harald, et al. “Methods for the Design and Development.” Lecture
Notes in Mechanical Engineering, 2014, doi:10.1007/978-3-642-45435-6_5.
short: 'H. Anacker, M. Dellnitz, K. Flaßkamp, S. Groesbrink, P. Hartmann, C. Heinzemann,
C. Horenkamp, B. Kleinjohann, L. Kleinjohann, S. Korf, M. Krüger, W. Müller, S.
Ober-Blöbaum, S. Oberthür, M. Porrmann, C. Priesterjahn, R. Radkowski, C. Rasche,
J. Rieke, M. Ringkamp, K. Stahl, D. Steenken, J. Stöcklein, R. Timmermann, A.
Trächtler, K. Witting, T. Xie, S. Ziegert, in: Lecture Notes in Mechanical Engineering,
Berlin, Heidelberg, 2014.'
date_created: 2020-04-16T10:23:51Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/978-3-642-45435-6_5
place: Berlin, Heidelberg
publication: Lecture Notes in Mechanical Engineering
publication_identifier:
isbn:
- '9783642454349'
- '9783642454356'
issn:
- 2195-4356
- 2195-4364
publication_status: published
status: public
title: Methods for the Design and Development
type: book_chapter
user_id: '15701'
year: '2014'
...
---
_id: '16576'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Florian
full_name: Dignath, Florian
last_name: Dignath
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Mirko Hessel-von
full_name: Molo, Mirko Hessel-von
last_name: Molo
- first_name: Martin
full_name: Krüger, Martin
last_name: Krüger
- first_name: Robert
full_name: Timmermann, Robert
last_name: Timmermann
- first_name: Qinghua
full_name: Zheng, Qinghua
last_name: Zheng
citation:
ama: 'Dellnitz M, Dignath F, Flaßkamp K, et al. Modelling and Analysis of the Nonlinear
Dynamics of the Transrapid and Its Guideway. In: Mathematics in Industry.
Berlin, Heidelberg; 2012. doi:10.1007/978-3-642-25100-9_14'
apa: Dellnitz, M., Dignath, F., Flaßkamp, K., Molo, M. H., Krüger, M., Timmermann,
R., & Zheng, Q. (2012). Modelling and Analysis of the Nonlinear Dynamics of
the Transrapid and Its Guideway. In Mathematics in Industry. Berlin, Heidelberg.
https://doi.org/10.1007/978-3-642-25100-9_14
bibtex: '@inbook{Dellnitz_Dignath_Flaßkamp_Molo_Krüger_Timmermann_Zheng_2012, place={Berlin,
Heidelberg}, title={Modelling and Analysis of the Nonlinear Dynamics of the Transrapid
and Its Guideway}, DOI={10.1007/978-3-642-25100-9_14},
booktitle={Mathematics in Industry}, author={Dellnitz, Michael and Dignath, Florian
and Flaßkamp, Kathrin and Molo, Mirko Hessel-von and Krüger, Martin and Timmermann,
Robert and Zheng, Qinghua}, year={2012} }'
chicago: Dellnitz, Michael, Florian Dignath, Kathrin Flaßkamp, Mirko Hessel-von
Molo, Martin Krüger, Robert Timmermann, and Qinghua Zheng. “Modelling and Analysis
of the Nonlinear Dynamics of the Transrapid and Its Guideway.” In Mathematics
in Industry. Berlin, Heidelberg, 2012. https://doi.org/10.1007/978-3-642-25100-9_14.
ieee: M. Dellnitz et al., “Modelling and Analysis of the Nonlinear Dynamics
of the Transrapid and Its Guideway,” in Mathematics in Industry, Berlin,
Heidelberg, 2012.
mla: Dellnitz, Michael, et al. “Modelling and Analysis of the Nonlinear Dynamics
of the Transrapid and Its Guideway.” Mathematics in Industry, 2012, doi:10.1007/978-3-642-25100-9_14.
short: 'M. Dellnitz, F. Dignath, K. Flaßkamp, M.H. Molo, M. Krüger, R. Timmermann,
Q. Zheng, in: Mathematics in Industry, Berlin, Heidelberg, 2012.'
date_created: 2020-04-16T05:08:17Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-3-642-25100-9_14
place: Berlin, Heidelberg
publication: Mathematics in Industry
publication_identifier:
isbn:
- '9783642250996'
- '9783642251009'
issn:
- 1612-3956
publication_status: published
status: public
title: Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its
Guideway
type: book_chapter
user_id: '15701'
year: '2012'
...
---
_id: '17035'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Florian
full_name: Dignath, Florian
last_name: Dignath
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Mirko Hessel-von
full_name: Molo, Mirko Hessel-von
last_name: Molo
- first_name: Martin
full_name: Krüger, Martin
last_name: Krüger
- first_name: Robert
full_name: Timmermann, Robert
last_name: Timmermann
- first_name: Qinghua
full_name: Zheng, Qinghua
last_name: Zheng
citation:
ama: 'Dellnitz M, Dignath F, Flaßkamp K, et al. Modelling and Analysis of the Nonlinear
Dynamics of the Transrapid and Its Guideway. In: Mathematics in Industry.
Berlin, Heidelberg; 2012. doi:10.1007/978-3-642-25100-9_14'
apa: Dellnitz, M., Dignath, F., Flaßkamp, K., Molo, M. H., Krüger, M., Timmermann,
R., & Zheng, Q. (2012). Modelling and Analysis of the Nonlinear Dynamics of
the Transrapid and Its Guideway. In Mathematics in Industry. Berlin, Heidelberg.
https://doi.org/10.1007/978-3-642-25100-9_14
bibtex: '@inbook{Dellnitz_Dignath_Flaßkamp_Molo_Krüger_Timmermann_Zheng_2012, place={Berlin,
Heidelberg}, title={Modelling and Analysis of the Nonlinear Dynamics of the Transrapid
and Its Guideway}, DOI={10.1007/978-3-642-25100-9_14},
booktitle={Mathematics in Industry}, author={Dellnitz, Michael and Dignath, Florian
and Flaßkamp, Kathrin and Molo, Mirko Hessel-von and Krüger, Martin and Timmermann,
Robert and Zheng, Qinghua}, year={2012} }'
chicago: Dellnitz, Michael, Florian Dignath, Kathrin Flaßkamp, Mirko Hessel-von
Molo, Martin Krüger, Robert Timmermann, and Qinghua Zheng. “Modelling and Analysis
of the Nonlinear Dynamics of the Transrapid and Its Guideway.” In Mathematics
in Industry. Berlin, Heidelberg, 2012. https://doi.org/10.1007/978-3-642-25100-9_14.
ieee: M. Dellnitz et al., “Modelling and Analysis of the Nonlinear Dynamics
of the Transrapid and Its Guideway,” in Mathematics in Industry, Berlin,
Heidelberg, 2012.
mla: Dellnitz, Michael, et al. “Modelling and Analysis of the Nonlinear Dynamics
of the Transrapid and Its Guideway.” Mathematics in Industry, 2012, doi:10.1007/978-3-642-25100-9_14.
short: 'M. Dellnitz, F. Dignath, K. Flaßkamp, M.H. Molo, M. Krüger, R. Timmermann,
Q. Zheng, in: Mathematics in Industry, Berlin, Heidelberg, 2012.'
date_created: 2020-05-20T08:04:20Z
date_updated: 2022-01-06T06:53:02Z
department:
- _id: '101'
doi: 10.1007/978-3-642-25100-9_14
language:
- iso: eng
place: Berlin, Heidelberg
publication: Mathematics in Industry
publication_identifier:
isbn:
- '9783642250996'
- '9783642251009'
issn:
- 1612-3956
publication_status: published
status: public
title: Modelling and Analysis of the Nonlinear Dynamics of the Transrapid and Its
Guideway
type: book_chapter
user_id: '47427'
year: '2012'
...
---
_id: '16528'
author:
- first_name: Alessandro
full_name: Dell'Aere, Alessandro
last_name: Dell'Aere
citation:
ama: 'Dell’Aere A. Multi-Objective Optimization in Self-Optimizing Systems. In:
IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics. ; 2006.
doi:10.1109/iecon.2006.348080'
apa: Dell’Aere, A. (2006). Multi-Objective Optimization in Self-Optimizing Systems.
In IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics.
https://doi.org/10.1109/iecon.2006.348080
bibtex: '@inproceedings{Dell’Aere_2006, title={Multi-Objective Optimization in Self-Optimizing
Systems}, DOI={10.1109/iecon.2006.348080},
booktitle={IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics},
author={Dell’Aere, Alessandro}, year={2006} }'
chicago: Dell’Aere, Alessandro. “Multi-Objective Optimization in Self-Optimizing
Systems.” In IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics,
2006. https://doi.org/10.1109/iecon.2006.348080.
ieee: A. Dell’Aere, “Multi-Objective Optimization in Self-Optimizing Systems,” in
IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics, 2006.
mla: Dell’Aere, Alessandro. “Multi-Objective Optimization in Self-Optimizing Systems.”
IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics, 2006,
doi:10.1109/iecon.2006.348080.
short: 'A. Dell’Aere, in: IECON 2006 - 32nd Annual Conference on IEEE Industrial
Electronics, 2006.'
date_created: 2020-04-15T08:19:05Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1109/iecon.2006.348080
language:
- iso: eng
publication: IECON 2006 - 32nd Annual Conference on IEEE Industrial Electronics
publication_identifier:
isbn:
- '1424403901'
- 142440391X
issn:
- 1553-572X
publication_status: published
status: public
title: Multi-Objective Optimization in Self-Optimizing Systems
type: conference
user_id: '15701'
year: '2006'
...
---
_id: '16695'
author:
- first_name: Fang
full_name: Wang, Fang
last_name: Wang
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Wang F, Dellnitz M. Multi-objective shape optimization for piezoceramics.
In: 2008 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications.
; 2009. doi:10.1109/spawda.2008.4775823'
apa: Wang, F., & Dellnitz, M. (2009). Multi-objective shape optimization for
piezoceramics. In 2008 Symposium on Piezoelectricity, Acoustic Waves, and Device
Applications. https://doi.org/10.1109/spawda.2008.4775823
bibtex: '@inproceedings{Wang_Dellnitz_2009, title={Multi-objective shape optimization
for piezoceramics}, DOI={10.1109/spawda.2008.4775823},
booktitle={2008 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications},
author={Wang, Fang and Dellnitz, Michael}, year={2009} }'
chicago: Wang, Fang, and Michael Dellnitz. “Multi-Objective Shape Optimization for
Piezoceramics.” In 2008 Symposium on Piezoelectricity, Acoustic Waves, and
Device Applications, 2009. https://doi.org/10.1109/spawda.2008.4775823.
ieee: F. Wang and M. Dellnitz, “Multi-objective shape optimization for piezoceramics,”
in 2008 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications,
2009.
mla: Wang, Fang, and Michael Dellnitz. “Multi-Objective Shape Optimization for Piezoceramics.”
2008 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications,
2009, doi:10.1109/spawda.2008.4775823.
short: 'F. Wang, M. Dellnitz, in: 2008 Symposium on Piezoelectricity, Acoustic Waves,
and Device Applications, 2009.'
date_created: 2020-04-16T10:50:00Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1109/spawda.2008.4775823
publication: 2008 Symposium on Piezoelectricity, Acoustic Waves, and Device Applications
publication_identifier:
isbn:
- '9781424428915'
publication_status: published
status: public
title: Multi-objective shape optimization for piezoceramics
type: conference
user_id: '15701'
year: '2009'
...
---
_id: '33150'
abstract:
- lang: eng
text: In this article, we build on previous work to present an optimization algorithm
for nonlinearly constrained multi-objective optimization problems. The algorithm
combines a surrogate-assisted derivative-free trust-region approach with the filter
method known from single-objective optimization. Instead of the true objective
and constraint functions, so-called fully linear models are employed and we show
how to deal with the gradient inexactness in the composite step setting, adapted
from single-objective optimization as well. Under standard assumptions, we prove
convergence of a subset of iterates to a quasi-stationary point and if constraint
qualifications hold, then the limit point is also a KKT-point of the multi-objective
problem.
author:
- first_name: Manuel Bastian
full_name: Berkemeier, Manuel Bastian
id: '51701'
last_name: Berkemeier
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Berkemeier MB, Peitz S. Multi-Objective Trust-Region Filter Method for Nonlinear
Constraints using Inexact Gradients. arXiv:220812094. Published online
2022.
apa: Berkemeier, M. B., & Peitz, S. (2022). Multi-Objective Trust-Region Filter
Method for Nonlinear Constraints using Inexact Gradients. In arXiv:2208.12094.
bibtex: '@article{Berkemeier_Peitz_2022, title={Multi-Objective Trust-Region Filter
Method for Nonlinear Constraints using Inexact Gradients}, journal={arXiv:2208.12094},
author={Berkemeier, Manuel Bastian and Peitz, Sebastian}, year={2022} }'
chicago: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region
Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094,
2022.
ieee: M. B. Berkemeier and S. Peitz, “Multi-Objective Trust-Region Filter Method
for Nonlinear Constraints using Inexact Gradients,” arXiv:2208.12094. 2022.
mla: Berkemeier, Manuel Bastian, and Sebastian Peitz. “Multi-Objective Trust-Region
Filter Method for Nonlinear Constraints Using Inexact Gradients.” ArXiv:2208.12094,
2022.
short: M.B. Berkemeier, S. Peitz, ArXiv:2208.12094 (2022).
date_created: 2022-08-26T06:08:06Z
date_updated: 2022-08-26T06:12:10Z
department:
- _id: '101'
- _id: '655'
external_id:
arxiv:
- '2208.12094'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2208.12094
oa: '1'
publication: arXiv:2208.12094
status: public
title: Multi-Objective Trust-Region Filter Method for Nonlinear Constraints using
Inexact Gradients
type: preprint
user_id: '47427'
year: '2022'
...
---
_id: '16681'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
citation:
ama: 'Dellnitz M, Schütze O. Multilevel Subdivision Techniques for Scalar Optimization
Problems. In: Global Analysis of Nonlinear Dynamics. New York, NY; 2012.
doi:10.1007/978-1-4614-3128-2_10'
apa: Dellnitz, M., & Schütze, O. (2012). Multilevel Subdivision Techniques for
Scalar Optimization Problems. In Global Analysis of Nonlinear Dynamics.
New York, NY. https://doi.org/10.1007/978-1-4614-3128-2_10
bibtex: '@inbook{Dellnitz_Schütze_2012, place={New York, NY}, title={Multilevel
Subdivision Techniques for Scalar Optimization Problems}, DOI={10.1007/978-1-4614-3128-2_10},
booktitle={Global Analysis of Nonlinear Dynamics}, author={Dellnitz, Michael and
Schütze, Oliver}, year={2012} }'
chicago: Dellnitz, Michael, and Oliver Schütze. “Multilevel Subdivision Techniques
for Scalar Optimization Problems.” In Global Analysis of Nonlinear Dynamics.
New York, NY, 2012. https://doi.org/10.1007/978-1-4614-3128-2_10.
ieee: M. Dellnitz and O. Schütze, “Multilevel Subdivision Techniques for Scalar
Optimization Problems,” in Global Analysis of Nonlinear Dynamics, New York,
NY, 2012.
mla: Dellnitz, Michael, and Oliver Schütze. “Multilevel Subdivision Techniques for
Scalar Optimization Problems.” Global Analysis of Nonlinear Dynamics, 2012,
doi:10.1007/978-1-4614-3128-2_10.
short: 'M. Dellnitz, O. Schütze, in: Global Analysis of Nonlinear Dynamics, New
York, NY, 2012.'
date_created: 2020-04-16T10:27:03Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/978-1-4614-3128-2_10
place: New York, NY
publication: Global Analysis of Nonlinear Dynamics
publication_identifier:
isbn:
- '9781461431275'
- '9781461431282'
publication_status: published
status: public
title: Multilevel Subdivision Techniques for Scalar Optimization Problems
type: book_chapter
user_id: '15701'
year: '2012'
...
---
_id: '8759'
abstract:
- lang: eng
text: In a wide range of applications, it is desirable to optimally control a system
with respect to concurrent, potentially competing goals. This gives rise to a
multiobjective optimal control problem where, instead of computing a single optimal
solution, the set of optimal compromises, the so-called Pareto set, has to be
approximated. When it is not possible to compute the entire control trajectory
in advance, for instance due to uncertainties or unforeseeable events, model predictive
control methods can be applied to control the system during operation in real
time. In this article, we present an algorithm for the solution of multiobjective
model predictive control problems. In an offline scenario, it can be used to compute
the entire set of optimal compromises whereas in a real time scenario, one optimal
compromise is computed according to an operator's preference. The results are
illustrated using the example of an industrial laundry. A logistics model of the
laundry is developed and then utilized in the optimization routine. Results are
presented for an offline as well as an online scenario.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Manuel
full_name: Gräler, Manuel
last_name: Gräler
- first_name: Christian
full_name: Henke, Christian
last_name: Henke
- first_name: Mirko Hessel-von
full_name: Molo, Mirko Hessel-von
last_name: Molo
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Ansgar
full_name: Trächtler, Ansgar
last_name: Trächtler
citation:
ama: 'Peitz S, Gräler M, Henke C, Molo MH, Dellnitz M, Trächtler A. Multiobjective
Model Predictive Control of an Industrial Laundry. In: Procedia Technology.
; 2016:483-490. doi:10.1016/j.protcy.2016.08.061'
apa: Peitz, S., Gräler, M., Henke, C., Molo, M. H., Dellnitz, M., & Trächtler,
A. (2016). Multiobjective Model Predictive Control of an Industrial Laundry. In
Procedia Technology (pp. 483–490). https://doi.org/10.1016/j.protcy.2016.08.061
bibtex: '@inproceedings{Peitz_Gräler_Henke_Molo_Dellnitz_Trächtler_2016, title={Multiobjective
Model Predictive Control of an Industrial Laundry}, DOI={10.1016/j.protcy.2016.08.061},
booktitle={Procedia Technology}, author={Peitz, Sebastian and Gräler, Manuel and
Henke, Christian and Molo, Mirko Hessel-von and Dellnitz, Michael and Trächtler,
Ansgar}, year={2016}, pages={483–490} }'
chicago: Peitz, Sebastian, Manuel Gräler, Christian Henke, Mirko Hessel-von Molo,
Michael Dellnitz, and Ansgar Trächtler. “Multiobjective Model Predictive Control
of an Industrial Laundry.” In Procedia Technology, 483–90, 2016. https://doi.org/10.1016/j.protcy.2016.08.061.
ieee: S. Peitz, M. Gräler, C. Henke, M. H. Molo, M. Dellnitz, and A. Trächtler,
“Multiobjective Model Predictive Control of an Industrial Laundry,” in Procedia
Technology, 2016, pp. 483–490.
mla: Peitz, Sebastian, et al. “Multiobjective Model Predictive Control of an Industrial
Laundry.” Procedia Technology, 2016, pp. 483–90, doi:10.1016/j.protcy.2016.08.061.
short: 'S. Peitz, M. Gräler, C. Henke, M.H. Molo, M. Dellnitz, A. Trächtler, in:
Procedia Technology, 2016, pp. 483–490.'
date_created: 2019-03-29T13:35:59Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.1016/j.protcy.2016.08.061
language:
- iso: eng
page: 483-490
publication: Procedia Technology
publication_identifier:
issn:
- 2212-0173
publication_status: published
status: public
title: Multiobjective Model Predictive Control of an Industrial Laundry
type: conference
user_id: '47427'
year: '2016'
...
---
_id: '34'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Julian
full_name: Eckstein, Julian
last_name: Eckstein
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Patrick
full_name: Friedel, Patrick
last_name: Friedel
- first_name: Christian
full_name: Horenkamp, Christian
last_name: Horenkamp
- first_name: Ulrich
full_name: Köhler, Ulrich
last_name: Köhler
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
last_name: Peitz
- first_name: Sebastian
full_name: Tiemeyer, Sebastian
last_name: Tiemeyer
citation:
ama: 'Dellnitz M, Eckstein J, Flaßkamp K, et al. Multiobjective Optimal Control
Methods for the Development of an Intelligent Cruise Control. In: Progress
in Industrial Mathematics at ECMI. Vol 22. Mathematics in Industry. Cham:
Springer International Publishing; 2016:633-641. doi:10.1007/978-3-319-23413-7_87'
apa: 'Dellnitz, M., Eckstein, J., Flaßkamp, K., Friedel, P., Horenkamp, C., Köhler,
U., … Tiemeyer, S. (2016). Multiobjective Optimal Control Methods for the Development
of an Intelligent Cruise Control. In Progress in Industrial Mathematics at
ECMI (Vol. 22, pp. 633–641). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-23413-7_87'
bibtex: '@inproceedings{Dellnitz_Eckstein_Flaßkamp_Friedel_Horenkamp_Köhler_Ober-Blöbaum_Peitz_Tiemeyer_2016,
place={Cham}, series={Mathematics in Industry}, title={Multiobjective Optimal
Control Methods for the Development of an Intelligent Cruise Control}, volume={22},
DOI={10.1007/978-3-319-23413-7_87},
booktitle={Progress in Industrial Mathematics at ECMI}, publisher={Springer International
Publishing}, author={Dellnitz, Michael and Eckstein, Julian and Flaßkamp, Kathrin
and Friedel, Patrick and Horenkamp, Christian and Köhler, Ulrich and Ober-Blöbaum,
Sina and Peitz, Sebastian and Tiemeyer, Sebastian}, year={2016}, pages={633–641},
collection={Mathematics in Industry} }'
chicago: 'Dellnitz, Michael, Julian Eckstein, Kathrin Flaßkamp, Patrick Friedel,
Christian Horenkamp, Ulrich Köhler, Sina Ober-Blöbaum, Sebastian Peitz, and Sebastian
Tiemeyer. “Multiobjective Optimal Control Methods for the Development of an Intelligent
Cruise Control.” In Progress in Industrial Mathematics at ECMI, 22:633–41.
Mathematics in Industry. Cham: Springer International Publishing, 2016. https://doi.org/10.1007/978-3-319-23413-7_87.'
ieee: M. Dellnitz et al., “Multiobjective Optimal Control Methods for the
Development of an Intelligent Cruise Control,” in Progress in Industrial Mathematics
at ECMI, 2016, vol. 22, pp. 633–641.
mla: Dellnitz, Michael, et al. “Multiobjective Optimal Control Methods for the Development
of an Intelligent Cruise Control.” Progress in Industrial Mathematics at ECMI,
vol. 22, Springer International Publishing, 2016, pp. 633–41, doi:10.1007/978-3-319-23413-7_87.
short: 'M. Dellnitz, J. Eckstein, K. Flaßkamp, P. Friedel, C. Horenkamp, U. Köhler,
S. Ober-Blöbaum, S. Peitz, S. Tiemeyer, in: Progress in Industrial Mathematics
at ECMI, Springer International Publishing, Cham, 2016, pp. 633–641.'
date_created: 2017-07-26T15:25:33Z
date_updated: 2022-01-06T06:59:14Z
department:
- _id: '27'
- _id: '101'
doi: 10.1007/978-3-319-23413-7_87
intvolume: ' 22'
page: 633-641
place: Cham
publication: Progress in Industrial Mathematics at ECMI
publication_identifier:
issn:
- 2212-0173
publisher: Springer International Publishing
series_title: Mathematics in Industry
status: public
title: Multiobjective Optimal Control Methods for the Development of an Intelligent
Cruise Control
type: conference
user_id: '24135'
volume: 22
year: '2016'
...
---
_id: '16579'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Julian
full_name: Eckstein, Julian
last_name: Eckstein
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Patrick
full_name: Friedel, Patrick
last_name: Friedel
- first_name: Christian
full_name: Horenkamp, Christian
last_name: Horenkamp
- first_name: Ulrich
full_name: Köhler, Ulrich
last_name: Köhler
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
last_name: Peitz
- first_name: Sebastian
full_name: Tiemeyer, Sebastian
last_name: Tiemeyer
citation:
ama: 'Dellnitz M, Eckstein J, Flaßkamp K, et al. Multiobjective Optimal Control
Methods for the Development of an Intelligent Cruise Control. In: Mathematics
in Industry. Cham; 2016. doi:10.1007/978-3-319-23413-7_87'
apa: Dellnitz, M., Eckstein, J., Flaßkamp, K., Friedel, P., Horenkamp, C., Köhler,
U., … Tiemeyer, S. (2016). Multiobjective Optimal Control Methods for the Development
of an Intelligent Cruise Control. In Mathematics in Industry. Cham. https://doi.org/10.1007/978-3-319-23413-7_87
bibtex: '@inbook{Dellnitz_Eckstein_Flaßkamp_Friedel_Horenkamp_Köhler_Ober-Blöbaum_Peitz_Tiemeyer_2016,
place={Cham}, title={Multiobjective Optimal Control Methods for the Development
of an Intelligent Cruise Control}, DOI={10.1007/978-3-319-23413-7_87},
booktitle={Mathematics in Industry}, author={Dellnitz, Michael and Eckstein, Julian
and Flaßkamp, Kathrin and Friedel, Patrick and Horenkamp, Christian and Köhler,
Ulrich and Ober-Blöbaum, Sina and Peitz, Sebastian and Tiemeyer, Sebastian}, year={2016}
}'
chicago: Dellnitz, Michael, Julian Eckstein, Kathrin Flaßkamp, Patrick Friedel,
Christian Horenkamp, Ulrich Köhler, Sina Ober-Blöbaum, Sebastian Peitz, and Sebastian
Tiemeyer. “Multiobjective Optimal Control Methods for the Development of an Intelligent
Cruise Control.” In Mathematics in Industry. Cham, 2016. https://doi.org/10.1007/978-3-319-23413-7_87.
ieee: M. Dellnitz et al., “Multiobjective Optimal Control Methods for the
Development of an Intelligent Cruise Control,” in Mathematics in Industry,
Cham, 2016.
mla: Dellnitz, Michael, et al. “Multiobjective Optimal Control Methods for the Development
of an Intelligent Cruise Control.” Mathematics in Industry, 2016, doi:10.1007/978-3-319-23413-7_87.
short: 'M. Dellnitz, J. Eckstein, K. Flaßkamp, P. Friedel, C. Horenkamp, U. Köhler,
S. Ober-Blöbaum, S. Peitz, S. Tiemeyer, in: Mathematics in Industry, Cham, 2016.'
date_created: 2020-04-16T05:37:11Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-3-319-23413-7_87
language:
- iso: eng
place: Cham
publication: Mathematics in Industry
publication_identifier:
isbn:
- '9783319234120'
- '9783319234137'
issn:
- 1612-3956
- 2198-3283
publication_status: published
status: public
title: Multiobjective Optimal Control Methods for the Development of an Intelligent
Cruise Control
type: book_chapter
user_id: '15701'
year: '2016'
...
---
_id: '8753'
abstract:
- lang: eng
text: In a wide range of applications it is desirable to optimally control a dynamical
system with respect to concurrent, potentially competing goals. This gives rise
to a multiobjective optimal control problem where, instead of computing a single
optimal solution, the set of optimal compromises, the so-called Pareto set, has
to be approximated. When the problem under consideration is described by a partial
differential equation (PDE), as is the case for fluid flow, the computational
cost rapidly increases and makes its direct treatment infeasible. Reduced order
modeling is a very popular method to reduce the computational cost, in particular
in a multi query context such as uncertainty quantification, parameter estimation
or optimization. In this article, we show how to combine reduced order modeling
and multiobjective optimal control techniques in order to efficiently solve multiobjective
optimal control problems constrained by PDEs. We consider a global, derivative
free optimization method as well as a local, gradient-based approach for which
the optimality system is derived in two different ways. The methods are compared
with regard to the solution quality as well as the computational effort and they
are illustrated using the example of the flow around a cylinder and a backward-facing-step
channel flow.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Peitz S, Ober-Blöbaum S, Dellnitz M. Multiobjective Optimal Control Methods
for the Navier-Stokes Equations Using Reduced Order Modeling. Acta Applicandae
Mathematicae. 2018;161(1):171–199. doi:10.1007/s10440-018-0209-7
apa: Peitz, S., Ober-Blöbaum, S., & Dellnitz, M. (2018). Multiobjective Optimal
Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.
Acta Applicandae Mathematicae, 161(1), 171–199. https://doi.org/10.1007/s10440-018-0209-7
bibtex: '@article{Peitz_Ober-Blöbaum_Dellnitz_2018, title={Multiobjective Optimal
Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling},
volume={161}, DOI={10.1007/s10440-018-0209-7},
number={1}, journal={Acta Applicandae Mathematicae}, author={Peitz, Sebastian
and Ober-Blöbaum, Sina and Dellnitz, Michael}, year={2018}, pages={171–199} }'
chicago: 'Peitz, Sebastian, Sina Ober-Blöbaum, and Michael Dellnitz. “Multiobjective
Optimal Control Methods for the Navier-Stokes Equations Using Reduced Order Modeling.”
Acta Applicandae Mathematicae 161, no. 1 (2018): 171–199. https://doi.org/10.1007/s10440-018-0209-7.'
ieee: 'S. Peitz, S. Ober-Blöbaum, and M. Dellnitz, “Multiobjective Optimal Control
Methods for the Navier-Stokes Equations Using Reduced Order Modeling,” Acta
Applicandae Mathematicae, vol. 161, no. 1, pp. 171–199, 2018, doi: 10.1007/s10440-018-0209-7.'
mla: Peitz, Sebastian, et al. “Multiobjective Optimal Control Methods for the Navier-Stokes
Equations Using Reduced Order Modeling.” Acta Applicandae Mathematicae,
vol. 161, no. 1, 2018, pp. 171–199, doi:10.1007/s10440-018-0209-7.
short: S. Peitz, S. Ober-Blöbaum, M. Dellnitz, Acta Applicandae Mathematicae 161
(2018) 171–199.
date_created: 2019-03-29T13:30:41Z
date_updated: 2022-01-21T10:01:41Z
department:
- _id: '101'
doi: 10.1007/s10440-018-0209-7
intvolume: ' 161'
issue: '1'
language:
- iso: eng
page: 171–199
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Acta Applicandae Mathematicae
publication_identifier:
issn:
- 0167-8019
- 1572-9036
publication_status: published
status: public
title: Multiobjective Optimal Control Methods for the Navier-Stokes Equations Using
Reduced Order Modeling
type: journal_article
user_id: '15694'
volume: 161
year: '2018'
...
---
_id: '16642'
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Padberg-Gehle, Kathrin
last_name: Padberg-Gehle
citation:
ama: Ober-Blöbaum S, Padberg-Gehle K. Multiobjective optimal control of fluid mixing.
PAMM. 2015:639-640. doi:10.1002/pamm.201510309
apa: Ober-Blöbaum, S., & Padberg-Gehle, K. (2015). Multiobjective optimal control
of fluid mixing. PAMM, 639–640. https://doi.org/10.1002/pamm.201510309
bibtex: '@article{Ober-Blöbaum_Padberg-Gehle_2015, title={Multiobjective optimal
control of fluid mixing}, DOI={10.1002/pamm.201510309},
journal={PAMM}, author={Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin}, year={2015},
pages={639–640} }'
chicago: Ober-Blöbaum, Sina, and Kathrin Padberg-Gehle. “Multiobjective Optimal
Control of Fluid Mixing.” PAMM, 2015, 639–40. https://doi.org/10.1002/pamm.201510309.
ieee: S. Ober-Blöbaum and K. Padberg-Gehle, “Multiobjective optimal control of fluid
mixing,” PAMM, pp. 639–640, 2015.
mla: Ober-Blöbaum, Sina, and Kathrin Padberg-Gehle. “Multiobjective Optimal Control
of Fluid Mixing.” PAMM, 2015, pp. 639–40, doi:10.1002/pamm.201510309.
short: S. Ober-Blöbaum, K. Padberg-Gehle, PAMM (2015) 639–640.
date_created: 2020-04-16T09:00:48Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1002/pamm.201510309
language:
- iso: eng
page: 639-640
publication: PAMM
publication_identifier:
issn:
- 1617-7061
publication_status: published
status: public
title: Multiobjective optimal control of fluid mixing
type: journal_article
user_id: '15701'
year: '2015'
...
---
_id: '16524'
author:
- first_name: Matthias
full_name: Blesken, Matthias
last_name: Blesken
- first_name: Ulrich
full_name: Ruckert, Ulrich
last_name: Ruckert
- first_name: Dominik
full_name: Steenken, Dominik
last_name: Steenken
- first_name: Katrin
full_name: Witting, Katrin
last_name: Witting
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Blesken M, Ruckert U, Steenken D, Witting K, Dellnitz M. Multiobjective optimization
for transistor sizing of CMOS logic standard cells using set-oriented numerical
techniques. In: 2009 NORCHIP. ; 2009. doi:10.1109/norchp.2009.5397800'
apa: Blesken, M., Ruckert, U., Steenken, D., Witting, K., & Dellnitz, M. (2009).
Multiobjective optimization for transistor sizing of CMOS logic standard cells
using set-oriented numerical techniques. In 2009 NORCHIP. https://doi.org/10.1109/norchp.2009.5397800
bibtex: '@inproceedings{Blesken_Ruckert_Steenken_Witting_Dellnitz_2009, title={Multiobjective
optimization for transistor sizing of CMOS logic standard cells using set-oriented
numerical techniques}, DOI={10.1109/norchp.2009.5397800},
booktitle={2009 NORCHIP}, author={Blesken, Matthias and Ruckert, Ulrich and Steenken,
Dominik and Witting, Katrin and Dellnitz, Michael}, year={2009} }'
chicago: Blesken, Matthias, Ulrich Ruckert, Dominik Steenken, Katrin Witting, and
Michael Dellnitz. “Multiobjective Optimization for Transistor Sizing of CMOS Logic
Standard Cells Using Set-Oriented Numerical Techniques.” In 2009 NORCHIP,
2009. https://doi.org/10.1109/norchp.2009.5397800.
ieee: M. Blesken, U. Ruckert, D. Steenken, K. Witting, and M. Dellnitz, “Multiobjective
optimization for transistor sizing of CMOS logic standard cells using set-oriented
numerical techniques,” in 2009 NORCHIP, 2009.
mla: Blesken, Matthias, et al. “Multiobjective Optimization for Transistor Sizing
of CMOS Logic Standard Cells Using Set-Oriented Numerical Techniques.” 2009
NORCHIP, 2009, doi:10.1109/norchp.2009.5397800.
short: 'M. Blesken, U. Ruckert, D. Steenken, K. Witting, M. Dellnitz, in: 2009 NORCHIP,
2009.'
date_created: 2020-04-15T08:11:10Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1109/norchp.2009.5397800
language:
- iso: eng
publication: 2009 NORCHIP
publication_identifier:
isbn:
- '9781424443109'
- '9781424443116'
publication_status: published
status: public
title: Multiobjective optimization for transistor sizing of CMOS logic standard cells
using set-oriented numerical techniques
type: conference
user_id: '15701'
year: '2009'
...
---
_id: '16610'
author:
- first_name: M.Sc. Jens
full_name: Geisler, M.Sc. Jens
last_name: Geisler
- first_name: Dipl.-Math. Katrin
full_name: Witting, Dipl.-Math. Katrin
last_name: Witting
- first_name: Ansgar
full_name: Trächtler, Ansgar
last_name: Trächtler
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Geisler MSJ, Witting D-MK, Trächtler A, Dellnitz M. Multiobjective Optimization
of Control Trajectories for the Guidance of a Rail-bound Vehicle. IFAC Proceedings
Volumes. 2008:4380-4386. doi:10.3182/20080706-5-kr-1001.00738
apa: Geisler, M. S. J., Witting, D.-M. K., Trächtler, A., & Dellnitz, M. (2008).
Multiobjective Optimization of Control Trajectories for the Guidance of a Rail-bound
Vehicle. IFAC Proceedings Volumes, 4380–4386. https://doi.org/10.3182/20080706-5-kr-1001.00738
bibtex: '@article{Geisler_Witting_Trächtler_Dellnitz_2008, title={Multiobjective
Optimization of Control Trajectories for the Guidance of a Rail-bound Vehicle},
DOI={10.3182/20080706-5-kr-1001.00738},
journal={IFAC Proceedings Volumes}, author={Geisler, M.Sc. Jens and Witting, Dipl.-Math.
Katrin and Trächtler, Ansgar and Dellnitz, Michael}, year={2008}, pages={4380–4386}
}'
chicago: Geisler, M.Sc. Jens, Dipl.-Math. Katrin Witting, Ansgar Trächtler, and
Michael Dellnitz. “Multiobjective Optimization of Control Trajectories for the
Guidance of a Rail-Bound Vehicle.” IFAC Proceedings Volumes, 2008, 4380–86.
https://doi.org/10.3182/20080706-5-kr-1001.00738.
ieee: M. S. J. Geisler, D.-M. K. Witting, A. Trächtler, and M. Dellnitz, “Multiobjective
Optimization of Control Trajectories for the Guidance of a Rail-bound Vehicle,”
IFAC Proceedings Volumes, pp. 4380–4386, 2008.
mla: Geisler, M. Sc. Jens, et al. “Multiobjective Optimization of Control Trajectories
for the Guidance of a Rail-Bound Vehicle.” IFAC Proceedings Volumes, 2008,
pp. 4380–86, doi:10.3182/20080706-5-kr-1001.00738.
short: M.S.J. Geisler, D.-M.K. Witting, A. Trächtler, M. Dellnitz, IFAC Proceedings
Volumes (2008) 4380–4386.
date_created: 2020-04-16T08:01:27Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.3182/20080706-5-kr-1001.00738
language:
- iso: eng
page: 4380-4386
publication: IFAC Proceedings Volumes
publication_identifier:
issn:
- 1474-6670
publication_status: published
status: public
title: Multiobjective Optimization of Control Trajectories for the Guidance of a Rail-bound
Vehicle
type: journal_article
user_id: '15701'
year: '2008'
...
---
_id: '46578'
abstract:
- lang: eng
text: 'Multiobjective optimization plays an increasingly important role in modern
applications, where several criteria are often of equal importance. The task in
multiobjective optimization and multiobjective optimal control is therefore to
compute the set of optimal compromises (the Pareto set) between the conflicting
objectives. The advances in algorithms and the increasing interest in Pareto-optimal
solutions have led to a wide range of new applications related to optimal and
feedback control - potentially with non-smoothness both on the level of the objectives
or in the system dynamics. This results in new challenges such as dealing with
expensive models (e.g., governed by partial differential equations (PDEs)) and
developing dedicated algorithms handling the non-smoothness. Since in contrast
to single-objective optimization, the Pareto set generally consists of an infinite
number of solutions, the computational effort can quickly become challenging,
which is particularly problematic when the objectives are costly to evaluate or
when a solution has to be presented very quickly. This article gives an overview
of recent developments in the field of multiobjective optimization of non-smooth
PDE-constrained problems. In particular we report on the advances achieved within
Project 2 "Multiobjective Optimization of Non-Smooth PDE-Constrained Problems
- Switches, State Constraints and Model Order Reduction" of the DFG Priority Programm
1962 "Non-smooth and Complementarity-based Distributed Parameter Systems: Simulation
and Hierarchical Optimization".'
author:
- first_name: Marco
full_name: Bernreuther, Marco
last_name: Bernreuther
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Georg
full_name: Müller, Georg
last_name: Müller
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Konstantin
full_name: Sonntag, Konstantin
id: '56399'
last_name: Sonntag
orcid: https://orcid.org/0000-0003-3384-3496
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: Bernreuther M, Dellnitz M, Gebken B, et al. Multiobjective Optimization of
Non-Smooth PDE-Constrained Problems. arXiv:230801113. Published online
2023.
apa: Bernreuther, M., Dellnitz, M., Gebken, B., Müller, G., Peitz, S., Sonntag,
K., & Volkwein, S. (2023). Multiobjective Optimization of Non-Smooth PDE-Constrained
Problems. In arXiv:2308.01113.
bibtex: '@article{Bernreuther_Dellnitz_Gebken_Müller_Peitz_Sonntag_Volkwein_2023,
title={Multiobjective Optimization of Non-Smooth PDE-Constrained Problems}, journal={arXiv:2308.01113},
author={Bernreuther, Marco and Dellnitz, Michael and Gebken, Bennet and Müller,
Georg and Peitz, Sebastian and Sonntag, Konstantin and Volkwein, Stefan}, year={2023}
}'
chicago: Bernreuther, Marco, Michael Dellnitz, Bennet Gebken, Georg Müller, Sebastian
Peitz, Konstantin Sonntag, and Stefan Volkwein. “Multiobjective Optimization of
Non-Smooth PDE-Constrained Problems.” ArXiv:2308.01113, 2023.
ieee: M. Bernreuther et al., “Multiobjective Optimization of Non-Smooth PDE-Constrained
Problems,” arXiv:2308.01113. 2023.
mla: Bernreuther, Marco, et al. “Multiobjective Optimization of Non-Smooth PDE-Constrained
Problems.” ArXiv:2308.01113, 2023.
short: M. Bernreuther, M. Dellnitz, B. Gebken, G. Müller, S. Peitz, K. Sonntag,
S. Volkwein, ArXiv:2308.01113 (2023).
date_created: 2023-08-21T05:50:12Z
date_updated: 2024-02-21T12:22:20Z
department:
- _id: '655'
- _id: '101'
external_id:
arxiv:
- '2308.01113'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/2308.01113
oa: '1'
publication: arXiv:2308.01113
status: public
title: Multiobjective Optimization of Non-Smooth PDE-Constrained Problems
type: preprint
user_id: '47427'
year: '2023'
...
---
_id: '1774'
abstract:
- lang: eng
text: In this article an efficient numerical method to solve multiobjective optimization
problems for fluid flow governed by the Navier Stokes equations is presented.
In order to decrease the computational effort, a reduced order model is introduced
using Proper Orthogonal Decomposition and a corresponding Galerkin Projection.
A global, derivative free multiobjective optimization algorithm is applied to
compute the Pareto set (i.e. the set of optimal compromises) for the concurrent
objectives minimization of flow field fluctuations and control cost. The method
is illustrated for a 2D flow around a cylinder at Re = 100.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
last_name: Peitz
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Peitz S, Dellnitz M. Multiobjective Optimization of the Flow Around a Cylinder
Using Model Order Reduction. PAMM. 2015;15(1):613-614. doi:10.1002/pamm.201510296
apa: Peitz, S., & Dellnitz, M. (2015). Multiobjective Optimization of the Flow
Around a Cylinder Using Model Order Reduction. PAMM, 15(1), 613–614.
https://doi.org/10.1002/pamm.201510296
bibtex: '@article{Peitz_Dellnitz_2015, title={Multiobjective Optimization of the
Flow Around a Cylinder Using Model Order Reduction}, volume={15}, DOI={10.1002/pamm.201510296},
number={1}, journal={PAMM}, publisher={WILEY-VCH Verlag}, author={Peitz, Sebastian
and Dellnitz, Michael}, year={2015}, pages={613–614} }'
chicago: 'Peitz, Sebastian, and Michael Dellnitz. “Multiobjective Optimization of
the Flow Around a Cylinder Using Model Order Reduction.” PAMM 15, no. 1
(2015): 613–14. https://doi.org/10.1002/pamm.201510296.'
ieee: S. Peitz and M. Dellnitz, “Multiobjective Optimization of the Flow Around
a Cylinder Using Model Order Reduction,” PAMM, vol. 15, no. 1, pp. 613–614,
2015.
mla: Peitz, Sebastian, and Michael Dellnitz. “Multiobjective Optimization of the
Flow Around a Cylinder Using Model Order Reduction.” PAMM, vol. 15, no.
1, WILEY-VCH Verlag, 2015, pp. 613–14, doi:10.1002/pamm.201510296.
short: S. Peitz, M. Dellnitz, PAMM 15 (2015) 613–614.
date_created: 2018-03-23T14:14:24Z
date_updated: 2022-01-06T06:53:19Z
department:
- _id: '27'
- _id: '101'
doi: 10.1002/pamm.201510296
intvolume: ' 15'
issue: '1'
page: 613-614
publication: PAMM
publication_identifier:
issn:
- 1617-7061
publisher: WILEY-VCH Verlag
status: public
title: Multiobjective Optimization of the Flow Around a Cylinder Using Model Order
Reduction
type: journal_article
user_id: '24135'
volume: 15
year: '2015'
...
---
_id: '8760'
abstract:
- lang: eng
text: n this article an efficient numerical method to solve multiobjective optimization
problems for fluid flow governed by the Navier Stokes equations is presented.
In order to decrease the computational effort, a reduced order model is introduced
using Proper Orthogonal Decomposition and a corresponding Galerkin Projection.
A global, derivative free multiobjective optimization algorithm is applied to
compute the Pareto set (i.e. the set of optimal compromises) for the concurrent
objectives minimization of flow field fluctuations and control cost. The method
is illustrated for a 2D flow around a cylinder at Re = 100.
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Peitz S, Dellnitz M. Multiobjective Optimization of the Flow Around a Cylinder
Using Model Order Reduction. In: PAMM. ; 2015:613-614. doi:10.1002/pamm.201510296'
apa: Peitz, S., & Dellnitz, M. (2015). Multiobjective Optimization of the Flow
Around a Cylinder Using Model Order Reduction. In PAMM (pp. 613–614). https://doi.org/10.1002/pamm.201510296
bibtex: '@inproceedings{Peitz_Dellnitz_2015, title={Multiobjective Optimization
of the Flow Around a Cylinder Using Model Order Reduction}, DOI={10.1002/pamm.201510296},
booktitle={PAMM}, author={Peitz, Sebastian and Dellnitz, Michael}, year={2015},
pages={613–614} }'
chicago: Peitz, Sebastian, and Michael Dellnitz. “Multiobjective Optimization of
the Flow Around a Cylinder Using Model Order Reduction.” In PAMM, 613–14,
2015. https://doi.org/10.1002/pamm.201510296.
ieee: S. Peitz and M. Dellnitz, “Multiobjective Optimization of the Flow Around
a Cylinder Using Model Order Reduction,” in PAMM, 2015, pp. 613–614.
mla: Peitz, Sebastian, and Michael Dellnitz. “Multiobjective Optimization of the
Flow Around a Cylinder Using Model Order Reduction.” PAMM, 2015, pp. 613–14,
doi:10.1002/pamm.201510296.
short: 'S. Peitz, M. Dellnitz, in: PAMM, 2015, pp. 613–614.'
date_created: 2019-03-29T13:36:33Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.1002/pamm.201510296
language:
- iso: eng
page: 613-614
publication: PAMM
publication_identifier:
issn:
- 1617-7061
publication_status: published
status: public
title: Multiobjective Optimization of the Flow Around a Cylinder Using Model Order
Reduction
type: conference
user_id: '47427'
year: '2015'
...
---
_id: '16521'
author:
- first_name: S.
full_name: Bezrukov, S.
last_name: Bezrukov
- first_name: R.
full_name: Elsässer, R.
last_name: Elsässer
- first_name: B.
full_name: Monien, B.
last_name: Monien
- first_name: R.
full_name: Preis, R.
last_name: Preis
- first_name: J.-P.
full_name: Tillich, J.-P.
last_name: Tillich
citation:
ama: Bezrukov S, Elsässer R, Monien B, Preis R, Tillich J-P. New spectral lower
bounds on the bisection width of graphs. Theoretical Computer Science.
2004:155-174. doi:10.1016/j.tcs.2004.03.059
apa: Bezrukov, S., Elsässer, R., Monien, B., Preis, R., & Tillich, J.-P. (2004).
New spectral lower bounds on the bisection width of graphs. Theoretical Computer
Science, 155–174. https://doi.org/10.1016/j.tcs.2004.03.059
bibtex: '@article{Bezrukov_Elsässer_Monien_Preis_Tillich_2004, title={New spectral
lower bounds on the bisection width of graphs}, DOI={10.1016/j.tcs.2004.03.059},
journal={Theoretical Computer Science}, author={Bezrukov, S. and Elsässer, R.
and Monien, B. and Preis, R. and Tillich, J.-P.}, year={2004}, pages={155–174}
}'
chicago: Bezrukov, S., R. Elsässer, B. Monien, R. Preis, and J.-P. Tillich. “New
Spectral Lower Bounds on the Bisection Width of Graphs.” Theoretical Computer
Science, 2004, 155–74. https://doi.org/10.1016/j.tcs.2004.03.059.
ieee: S. Bezrukov, R. Elsässer, B. Monien, R. Preis, and J.-P. Tillich, “New spectral
lower bounds on the bisection width of graphs,” Theoretical Computer Science,
pp. 155–174, 2004.
mla: Bezrukov, S., et al. “New Spectral Lower Bounds on the Bisection Width of Graphs.”
Theoretical Computer Science, 2004, pp. 155–74, doi:10.1016/j.tcs.2004.03.059.
short: S. Bezrukov, R. Elsässer, B. Monien, R. Preis, J.-P. Tillich, Theoretical
Computer Science (2004) 155–174.
date_created: 2020-04-15T08:05:40Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1016/j.tcs.2004.03.059
language:
- iso: eng
page: 155-174
publication: Theoretical Computer Science
publication_identifier:
issn:
- 0304-3975
publication_status: published
status: public
title: New spectral lower bounds on the bisection width of graphs
type: journal_article
user_id: '15701'
year: '2004'
...
---
_id: '16516'
author:
- first_name: Robert
full_name: Baier, Robert
last_name: Baier
- first_name: Mirko Hessel-von
full_name: Molo, Mirko Hessel-von
last_name: Molo
citation:
ama: 'Baier R, Molo MH. Newton’s Method and Secant Method for Set-Valued Mappings.
In: Large-Scale Scientific Computing. Berlin, Heidelberg; 2012. doi:10.1007/978-3-642-29843-1_9'
apa: Baier, R., & Molo, M. H. (2012). Newton’s Method and Secant Method for
Set-Valued Mappings. In Large-Scale Scientific Computing. Berlin, Heidelberg.
https://doi.org/10.1007/978-3-642-29843-1_9
bibtex: '@inbook{Baier_Molo_2012, place={Berlin, Heidelberg}, title={Newton’s Method
and Secant Method for Set-Valued Mappings}, DOI={10.1007/978-3-642-29843-1_9},
booktitle={Large-Scale Scientific Computing}, author={Baier, Robert and Molo,
Mirko Hessel-von}, year={2012} }'
chicago: Baier, Robert, and Mirko Hessel-von Molo. “Newton’s Method and Secant Method
for Set-Valued Mappings.” In Large-Scale Scientific Computing. Berlin,
Heidelberg, 2012. https://doi.org/10.1007/978-3-642-29843-1_9.
ieee: R. Baier and M. H. Molo, “Newton’s Method and Secant Method for Set-Valued
Mappings,” in Large-Scale Scientific Computing, Berlin, Heidelberg, 2012.
mla: Baier, Robert, and Mirko Hessel-von Molo. “Newton’s Method and Secant Method
for Set-Valued Mappings.” Large-Scale Scientific Computing, 2012, doi:10.1007/978-3-642-29843-1_9.
short: 'R. Baier, M.H. Molo, in: Large-Scale Scientific Computing, Berlin, Heidelberg,
2012.'
date_created: 2020-04-15T07:59:49Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-3-642-29843-1_9
place: Berlin, Heidelberg
publication: Large-Scale Scientific Computing
publication_identifier:
isbn:
- '9783642298424'
- '9783642298431'
issn:
- 0302-9743
- 1611-3349
publication_status: published
status: public
title: Newton’s Method and Secant Method for Set-Valued Mappings
type: book_chapter
user_id: '15701'
year: '2012'
...
---
_id: '16633'
abstract:
- lang: eng
text: AbstractWe obtain normal forms for infinitesimally
symplectic matrices (or linear Hamiltonian vector fields) that commute with the
symplectic action of a compact Lie group of symmetries. In doing so we extend
Williamson's theorem on normal forms when there is no symmetry present.Using
standard representation-theoretic results the symmetry can be factored out and
we reduce to finding normal forms over a real division ring. There are three real
division rings consisting of the real, complex and quaternionic numbers. Of these,
only the real case is covered in Williamson's original work.
author:
- first_name: Ian
full_name: Melbourne, Ian
last_name: Melbourne
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Melbourne I, Dellnitz M. Normal forms for linear Hamiltonian vector fields
commuting with the action of a compact Lie group. Mathematical Proceedings
of the Cambridge Philosophical Society. 1993:235-268. doi:10.1017/s0305004100071577
apa: Melbourne, I., & Dellnitz, M. (1993). Normal forms for linear Hamiltonian
vector fields commuting with the action of a compact Lie group. Mathematical
Proceedings of the Cambridge Philosophical Society, 235–268. https://doi.org/10.1017/s0305004100071577
bibtex: '@article{Melbourne_Dellnitz_1993, title={Normal forms for linear Hamiltonian
vector fields commuting with the action of a compact Lie group}, DOI={10.1017/s0305004100071577},
journal={Mathematical Proceedings of the Cambridge Philosophical Society}, author={Melbourne,
Ian and Dellnitz, Michael}, year={1993}, pages={235–268} }'
chicago: Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian
Vector Fields Commuting with the Action of a Compact Lie Group.” Mathematical
Proceedings of the Cambridge Philosophical Society, 1993, 235–68. https://doi.org/10.1017/s0305004100071577.
ieee: I. Melbourne and M. Dellnitz, “Normal forms for linear Hamiltonian vector
fields commuting with the action of a compact Lie group,” Mathematical Proceedings
of the Cambridge Philosophical Society, pp. 235–268, 1993.
mla: Melbourne, Ian, and Michael Dellnitz. “Normal Forms for Linear Hamiltonian
Vector Fields Commuting with the Action of a Compact Lie Group.” Mathematical
Proceedings of the Cambridge Philosophical Society, 1993, pp. 235–68, doi:10.1017/s0305004100071577.
short: I. Melbourne, M. Dellnitz, Mathematical Proceedings of the Cambridge Philosophical
Society (1993) 235–268.
date_created: 2020-04-16T08:31:40Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1017/s0305004100071577
language:
- iso: eng
page: 235-268
publication: Mathematical Proceedings of the Cambridge Philosophical Society
publication_identifier:
issn:
- 0305-0041
- 1469-8064
publication_status: published
status: public
title: Normal forms for linear Hamiltonian vector fields commuting with the action
of a compact Lie group
type: journal_article
user_id: '15701'
year: '1993'
...
---
_id: '16560'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Marcus
full_name: Post, Marcus
last_name: Post
- first_name: Bianca
full_name: Thiere, Bianca
last_name: Thiere
citation:
ama: Dellnitz M, Junge O, Post M, Thiere B. On target for Venus – set oriented computation
of energy efficient low thrust trajectories. Celestial Mechanics and Dynamical
Astronomy. 2006:357-370. doi:10.1007/s10569-006-9008-y
apa: Dellnitz, M., Junge, O., Post, M., & Thiere, B. (2006). On target for Venus
– set oriented computation of energy efficient low thrust trajectories. Celestial
Mechanics and Dynamical Astronomy, 357–370. https://doi.org/10.1007/s10569-006-9008-y
bibtex: '@article{Dellnitz_Junge_Post_Thiere_2006, title={On target for Venus –
set oriented computation of energy efficient low thrust trajectories}, DOI={10.1007/s10569-006-9008-y},
journal={Celestial Mechanics and Dynamical Astronomy}, author={Dellnitz, Michael
and Junge, Oliver and Post, Marcus and Thiere, Bianca}, year={2006}, pages={357–370}
}'
chicago: Dellnitz, Michael, Oliver Junge, Marcus Post, and Bianca Thiere. “On Target
for Venus – Set Oriented Computation of Energy Efficient Low Thrust Trajectories.”
Celestial Mechanics and Dynamical Astronomy, 2006, 357–70. https://doi.org/10.1007/s10569-006-9008-y.
ieee: M. Dellnitz, O. Junge, M. Post, and B. Thiere, “On target for Venus – set
oriented computation of energy efficient low thrust trajectories,” Celestial
Mechanics and Dynamical Astronomy, pp. 357–370, 2006.
mla: Dellnitz, Michael, et al. “On Target for Venus – Set Oriented Computation of
Energy Efficient Low Thrust Trajectories.” Celestial Mechanics and Dynamical
Astronomy, 2006, pp. 357–70, doi:10.1007/s10569-006-9008-y.
short: M. Dellnitz, O. Junge, M. Post, B. Thiere, Celestial Mechanics and Dynamical
Astronomy (2006) 357–370.
date_created: 2020-04-15T09:58:17Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/s10569-006-9008-y
language:
- iso: eng
page: 357-370
publication: Celestial Mechanics and Dynamical Astronomy
publication_identifier:
issn:
- 0923-2958
- 1572-9478
publication_status: published
status: public
title: On target for Venus – set oriented computation of energy efficient low thrust
trajectories
type: journal_article
user_id: '15701'
year: '2006'
...
---
_id: '16537'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: Dellnitz M, Junge O. On the Approximation of Complicated Dynamical Behavior.
SIAM Journal on Numerical Analysis. 1999:491-515. doi:10.1137/s0036142996313002
apa: Dellnitz, M., & Junge, O. (1999). On the Approximation of Complicated Dynamical
Behavior. SIAM Journal on Numerical Analysis, 491–515. https://doi.org/10.1137/s0036142996313002
bibtex: '@article{Dellnitz_Junge_1999, title={On the Approximation of Complicated
Dynamical Behavior}, DOI={10.1137/s0036142996313002},
journal={SIAM Journal on Numerical Analysis}, author={Dellnitz, Michael and Junge,
Oliver}, year={1999}, pages={491–515} }'
chicago: Dellnitz, Michael, and Oliver Junge. “On the Approximation of Complicated
Dynamical Behavior.” SIAM Journal on Numerical Analysis, 1999, 491–515.
https://doi.org/10.1137/s0036142996313002.
ieee: M. Dellnitz and O. Junge, “On the Approximation of Complicated Dynamical Behavior,”
SIAM Journal on Numerical Analysis, pp. 491–515, 1999.
mla: Dellnitz, Michael, and Oliver Junge. “On the Approximation of Complicated Dynamical
Behavior.” SIAM Journal on Numerical Analysis, 1999, pp. 491–515, doi:10.1137/s0036142996313002.
short: M. Dellnitz, O. Junge, SIAM Journal on Numerical Analysis (1999) 491–515.
date_created: 2020-04-15T08:35:45Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1137/s0036142996313002
language:
- iso: eng
page: 491-515
publication: SIAM Journal on Numerical Analysis
publication_identifier:
issn:
- 0036-1429
- 1095-7170
publication_status: published
status: public
title: On the Approximation of Complicated Dynamical Behavior
type: journal_article
user_id: '15701'
year: '1999'
...
---
_id: '16572'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Christian
full_name: Horenkamp, Christian
last_name: Horenkamp
- first_name: Kathrin
full_name: Padberg, Kathrin
last_name: Padberg
citation:
ama: Dellnitz M, Froyland G, Horenkamp C, Padberg K. On the Approximation of Transport
Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen. 2009:47-60.
doi:10.1002/gamm.200910004
apa: Dellnitz, M., Froyland, G., Horenkamp, C., & Padberg, K. (2009). On the
Approximation of Transport Phenomena - a Dynamical Systems Approach. GAMM-Mitteilungen,
47–60. https://doi.org/10.1002/gamm.200910004
bibtex: '@article{Dellnitz_Froyland_Horenkamp_Padberg_2009, title={On the Approximation
of Transport Phenomena - a Dynamical Systems Approach}, DOI={10.1002/gamm.200910004},
journal={GAMM-Mitteilungen}, author={Dellnitz, Michael and Froyland, Gary and
Horenkamp, Christian and Padberg, Kathrin}, year={2009}, pages={47–60} }'
chicago: Dellnitz, Michael, Gary Froyland, Christian Horenkamp, and Kathrin Padberg.
“On the Approximation of Transport Phenomena - a Dynamical Systems Approach.”
GAMM-Mitteilungen, 2009, 47–60. https://doi.org/10.1002/gamm.200910004.
ieee: M. Dellnitz, G. Froyland, C. Horenkamp, and K. Padberg, “On the Approximation
of Transport Phenomena - a Dynamical Systems Approach,” GAMM-Mitteilungen,
pp. 47–60, 2009.
mla: Dellnitz, Michael, et al. “On the Approximation of Transport Phenomena - a
Dynamical Systems Approach.” GAMM-Mitteilungen, 2009, pp. 47–60, doi:10.1002/gamm.200910004.
short: M. Dellnitz, G. Froyland, C. Horenkamp, K. Padberg, GAMM-Mitteilungen (2009)
47–60.
date_created: 2020-04-16T05:01:31Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1002/gamm.200910004
language:
- iso: eng
page: 47-60
publication: GAMM-Mitteilungen
publication_identifier:
issn:
- 0936-7195
- 1522-2608
publication_status: published
status: public
title: On the Approximation of Transport Phenomena - a Dynamical Systems Approach
type: journal_article
user_id: '15701'
year: '2009'
...
---
_id: '16580'
author:
- first_name: Adrian
full_name: Ziessler, Adrian
last_name: Ziessler
- first_name: Mirko Hessel-Von
full_name: Molo, Mirko Hessel-Von
last_name: Molo
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Ziessler A, Molo MH-V, Dellnitz M. On the computation of attractors for delay
differential equations. Journal of Computational Dynamics. 2016:5-5. doi:10.3934/jcd.2016005
apa: Ziessler, A., Molo, M. H.-V., & Dellnitz, M. (2016). On the computation
of attractors for delay differential equations. Journal of Computational Dynamics,
5–5. https://doi.org/10.3934/jcd.2016005
bibtex: '@article{Ziessler_Molo_Dellnitz_2016, title={On the computation of attractors
for delay differential equations}, DOI={10.3934/jcd.2016005},
journal={Journal of Computational Dynamics}, author={Ziessler, Adrian and Molo,
Mirko Hessel-Von and Dellnitz, Michael}, year={2016}, pages={5–5} }'
chicago: Ziessler, Adrian, Mirko Hessel-Von Molo, and Michael Dellnitz. “On the
Computation of Attractors for Delay Differential Equations.” Journal of Computational
Dynamics, 2016, 5–5. https://doi.org/10.3934/jcd.2016005.
ieee: A. Ziessler, M. H.-V. Molo, and M. Dellnitz, “On the computation of attractors
for delay differential equations,” Journal of Computational Dynamics, pp.
5–5, 2016.
mla: Ziessler, Adrian, et al. “On the Computation of Attractors for Delay Differential
Equations.” Journal of Computational Dynamics, 2016, pp. 5–5, doi:10.3934/jcd.2016005.
short: A. Ziessler, M.H.-V. Molo, M. Dellnitz, Journal of Computational Dynamics
(2016) 5–5.
date_created: 2020-04-16T05:38:13Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.3934/jcd.2016005
language:
- iso: eng
page: 5-5
publication: Journal of Computational Dynamics
publication_identifier:
issn:
- 2158-2491
publication_status: published
status: public
title: On the computation of attractors for delay differential equations
type: journal_article
user_id: '15701'
year: '2016'
...
---
_id: '44840'
abstract:
- lang: eng
text: "In this article we investigate the convergence behavior of gathering protocols
with fixed circulant topologies using tools form dynamical systems. Given a fixed
number of mobile entities moving in the Euclidean plane, we model a gathering
protocol as a system of ordinary differential equations whose equilibria are exactly
all possible gathering points. Then, we find necessary and sufficient conditions
for the structure of the underlying interaction graph such that the protocol is
stable and converging, i.e., gathering, in the distributive computing sense by
using tools from dynamical systems. Moreover, these tools allow for a more fine
grained analysis in terms of speed of convergence in the dynamical systems sense.
In fact, we derive a decomposition\r\nof the state space into stable invariant
subspaces with different convergence\r\nrates. In particular, this decomposition
is identical for every (linear)\r\ncirculant gathering protocol, whereas only
the convergence rates depend on the\r\nweights in interaction graph itself."
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
- first_name: Sören
full_name: von der Gracht, Sören
id: '97359'
last_name: von der Gracht
orcid: 0000-0002-8054-2058
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Gerlach R, von der Gracht S, Dellnitz M. On the Dynamical Hierarchy in Gathering
Protocols with Circulant Topologies. arXiv:230506632.
apa: Gerlach, R., von der Gracht, S., & Dellnitz, M. (n.d.). On the Dynamical
Hierarchy in Gathering Protocols with Circulant Topologies. In arXiv:2305.06632.
bibtex: '@article{Gerlach_von der Gracht_Dellnitz, title={On the Dynamical Hierarchy
in Gathering Protocols with Circulant Topologies}, journal={arXiv:2305.06632},
author={Gerlach, Raphael and von der Gracht, Sören and Dellnitz, Michael} }'
chicago: Gerlach, Raphael, Sören von der Gracht, and Michael Dellnitz. “On the Dynamical
Hierarchy in Gathering Protocols with Circulant Topologies.” ArXiv:2305.06632,
n.d.
ieee: R. Gerlach, S. von der Gracht, and M. Dellnitz, “On the Dynamical Hierarchy
in Gathering Protocols with Circulant Topologies,” arXiv:2305.06632. .
mla: Gerlach, Raphael, et al. “On the Dynamical Hierarchy in Gathering Protocols
with Circulant Topologies.” ArXiv:2305.06632.
short: R. Gerlach, S. von der Gracht, M. Dellnitz, ArXiv:2305.06632 (n.d.).
date_created: 2023-05-12T10:16:06Z
date_updated: 2024-01-03T17:00:48Z
department:
- _id: '101'
external_id:
arxiv:
- '2305.06632'
keyword:
- Dynamical Systems
- Coupled Systems
- Distributed Computing
- Robot Swarms
- Autonomous Mobile Robots
- Gathering
language:
- iso: eng
main_file_link:
- url: https://arxiv.org/abs/2305.06632
page: '38'
project:
- _id: '106'
grant_number: '453112019'
name: 'Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme'
publication: arXiv:2305.06632
publication_status: submitted
related_material:
link:
- relation: supplementary_material
url: https://math.uni-paderborn.de/en/ag/chair-of-applied-mathematics/research/research-projects/swarmdynamics
status: public
title: On the Dynamical Hierarchy in Gathering Protocols with Circulant Topologies
type: preprint
user_id: '32655'
year: '2023'
...
---
_id: '16712'
abstract:
- lang: eng
text: We investigate self-adjoint matrices A∈Rn,n with respect to their equivariance
properties. We show in particular that a matrix is self-adjoint if and only if
it is equivariant with respect to the action of a group Γ2(A)⊂O(n) which is isomorphic
to ⊗nk=1Z2. If the self-adjoint matrix possesses multiple eigenvalues – this may,
for instance, be induced by symmetry properties of an underlying dynamical system
– then A is even equivariant with respect to the action of a group Γ(A)≃∏ki=1O(mi)
where m1,…,mk are the multiplicities of the eigenvalues λ1,…,λk of A. We discuss
implications of this result for equivariant bifurcation problems, and we briefly
address further applications for the Procrustes problem, graph symmetries and
Taylor expansions.
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
citation:
ama: Dellnitz M, Gebken B, Gerlach R, Klus S. On the equivariance properties of
self-adjoint matrices. Dynamical Systems. 2020;35(2):197-215. doi:10.1080/14689367.2019.1661355
apa: Dellnitz, M., Gebken, B., Gerlach, R., & Klus, S. (2020). On the equivariance
properties of self-adjoint matrices. Dynamical Systems, 35(2), 197–215.
https://doi.org/10.1080/14689367.2019.1661355
bibtex: '@article{Dellnitz_Gebken_Gerlach_Klus_2020, title={On the equivariance
properties of self-adjoint matrices}, volume={35}, DOI={10.1080/14689367.2019.1661355},
number={2}, journal={Dynamical Systems}, author={Dellnitz, Michael and Gebken,
Bennet and Gerlach, Raphael and Klus, Stefan}, year={2020}, pages={197–215} }'
chicago: 'Dellnitz, Michael, Bennet Gebken, Raphael Gerlach, and Stefan Klus. “On
the Equivariance Properties of Self-Adjoint Matrices.” Dynamical Systems
35, no. 2 (2020): 197–215. https://doi.org/10.1080/14689367.2019.1661355.'
ieee: 'M. Dellnitz, B. Gebken, R. Gerlach, and S. Klus, “On the equivariance properties
of self-adjoint matrices,” Dynamical Systems, vol. 35, no. 2, pp. 197–215,
2020, doi: 10.1080/14689367.2019.1661355.'
mla: Dellnitz, Michael, et al. “On the Equivariance Properties of Self-Adjoint Matrices.”
Dynamical Systems, vol. 35, no. 2, 2020, pp. 197–215, doi:10.1080/14689367.2019.1661355.
short: M. Dellnitz, B. Gebken, R. Gerlach, S. Klus, Dynamical Systems 35 (2020)
197–215.
date_created: 2020-04-16T14:07:25Z
date_updated: 2023-11-17T13:12:59Z
department:
- _id: '101'
doi: 10.1080/14689367.2019.1661355
intvolume: ' 35'
issue: '2'
language:
- iso: eng
main_file_link:
- url: https://doi.org/10.1080/14689367.2019.1661355
page: 197-215
publication: Dynamical Systems
publication_identifier:
issn:
- 1468-9367
- 1468-9375
publication_status: published
status: public
title: On the equivariance properties of self-adjoint matrices
type: journal_article
user_id: '32655'
volume: 35
year: '2020'
...
---
_id: '10595'
abstract:
- lang: eng
text: In this article we show that the boundary of the Pareto critical set of an
unconstrained multiobjective optimization problem (MOP) consists of Pareto critical
points of subproblems where only a subset of the set of objective functions is
taken into account. If the Pareto critical set is completely described by its
boundary (e.g., if we have more objective functions than dimensions in decision
space), then this can be used to efficiently solve the MOP by solving a number
of MOPs with fewer objective functions. If this is not the case, the results can
still give insight into the structure of the Pareto critical set.
article_type: original
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Gebken B, Peitz S, Dellnitz M. On the hierarchical structure of Pareto critical
sets. Journal of Global Optimization. 2019;73(4):891-913. doi:10.1007/s10898-019-00737-6
apa: Gebken, B., Peitz, S., & Dellnitz, M. (2019). On the hierarchical structure
of Pareto critical sets. Journal of Global Optimization, 73(4),
891–913. https://doi.org/10.1007/s10898-019-00737-6
bibtex: '@article{Gebken_Peitz_Dellnitz_2019, title={On the hierarchical structure
of Pareto critical sets}, volume={73}, DOI={10.1007/s10898-019-00737-6},
number={4}, journal={Journal of Global Optimization}, author={Gebken, Bennet and
Peitz, Sebastian and Dellnitz, Michael}, year={2019}, pages={891–913} }'
chicago: 'Gebken, Bennet, Sebastian Peitz, and Michael Dellnitz. “On the Hierarchical
Structure of Pareto Critical Sets.” Journal of Global Optimization 73,
no. 4 (2019): 891–913. https://doi.org/10.1007/s10898-019-00737-6.'
ieee: B. Gebken, S. Peitz, and M. Dellnitz, “On the hierarchical structure of Pareto
critical sets,” Journal of Global Optimization, vol. 73, no. 4, pp. 891–913,
2019.
mla: Gebken, Bennet, et al. “On the Hierarchical Structure of Pareto Critical Sets.”
Journal of Global Optimization, vol. 73, no. 4, 2019, pp. 891–913, doi:10.1007/s10898-019-00737-6.
short: B. Gebken, S. Peitz, M. Dellnitz, Journal of Global Optimization 73 (2019)
891–913.
date_created: 2019-07-10T08:13:31Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1007/s10898-019-00737-6
intvolume: ' 73'
issue: '4'
language:
- iso: eng
page: 891-913
publication: Journal of Global Optimization
publication_identifier:
issn:
- 0925-5001
- 1573-2916
publication_status: published
status: public
title: On the hierarchical structure of Pareto critical sets
type: journal_article
user_id: '47427'
volume: 73
year: '2019'
...
---
_id: '16554'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Stefan
full_name: Sertl, Stefan
last_name: Sertl
citation:
ama: Dellnitz M, Froyland G, Sertl S. On the isolated spectrum of the Perron-Frobenius
operator. Nonlinearity. 2000:1171-1188. doi:10.1088/0951-7715/13/4/310
apa: Dellnitz, M., Froyland, G., & Sertl, S. (2000). On the isolated spectrum
of the Perron-Frobenius operator. Nonlinearity, 1171–1188. https://doi.org/10.1088/0951-7715/13/4/310
bibtex: '@article{Dellnitz_Froyland_Sertl_2000, title={On the isolated spectrum
of the Perron-Frobenius operator}, DOI={10.1088/0951-7715/13/4/310},
journal={Nonlinearity}, author={Dellnitz, Michael and Froyland, Gary and Sertl,
Stefan}, year={2000}, pages={1171–1188} }'
chicago: Dellnitz, Michael, Gary Froyland, and Stefan Sertl. “On the Isolated Spectrum
of the Perron-Frobenius Operator.” Nonlinearity, 2000, 1171–88. https://doi.org/10.1088/0951-7715/13/4/310.
ieee: M. Dellnitz, G. Froyland, and S. Sertl, “On the isolated spectrum of the Perron-Frobenius
operator,” Nonlinearity, pp. 1171–1188, 2000.
mla: Dellnitz, Michael, et al. “On the Isolated Spectrum of the Perron-Frobenius
Operator.” Nonlinearity, 2000, pp. 1171–88, doi:10.1088/0951-7715/13/4/310.
short: M. Dellnitz, G. Froyland, S. Sertl, Nonlinearity (2000) 1171–1188.
date_created: 2020-04-15T09:09:46Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1088/0951-7715/13/4/310
language:
- iso: eng
page: 1171-1188
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: On the isolated spectrum of the Perron-Frobenius operator
type: journal_article
user_id: '15701'
year: '2000'
...
---
_id: '17045'
author:
- first_name: Tobias
full_name: Gail, Tobias
last_name: Gail
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
citation:
ama: 'Gail T, Leyendecker S, Ober-Blöbaum S. On the role of quadrature rules and
system dimensions in variational multirateintegrators. In: The 3rdJoint International
Conference on Multibody System Dynamics. ; 2014.'
apa: Gail, T., Leyendecker, S., & Ober-Blöbaum, S. (2014). On the role of quadrature
rules and system dimensions in variational multirateintegrators. In The 3rdJoint
International Conference on Multibody System Dynamics.
bibtex: '@inproceedings{Gail_Leyendecker_Ober-Blöbaum_2014, title={On the role of
quadrature rules and system dimensions in variational multirateintegrators}, booktitle={The
3rdJoint International Conference on Multibody System Dynamics}, author={Gail,
Tobias and Leyendecker, Sigrid and Ober-Blöbaum, Sina}, year={2014} }'
chicago: Gail, Tobias, Sigrid Leyendecker, and Sina Ober-Blöbaum. “On the Role of
Quadrature Rules and System Dimensions in Variational Multirateintegrators.” In
The 3rdJoint International Conference on Multibody System Dynamics, 2014.
ieee: T. Gail, S. Leyendecker, and S. Ober-Blöbaum, “On the role of quadrature rules
and system dimensions in variational multirateintegrators,” in The 3rdJoint
International Conference on Multibody System Dynamics, 2014.
mla: Gail, Tobias, et al. “On the Role of Quadrature Rules and System Dimensions
in Variational Multirateintegrators.” The 3rdJoint International Conference
on Multibody System Dynamics, 2014.
short: 'T. Gail, S. Leyendecker, S. Ober-Blöbaum, in: The 3rdJoint International
Conference on Multibody System Dynamics, 2014.'
date_created: 2020-05-20T08:32:33Z
date_updated: 2022-01-06T06:53:03Z
department:
- _id: '101'
language:
- iso: eng
publication: The 3rdJoint International Conference on Multibody System Dynamics
status: public
title: On the role of quadrature rules and system dimensions in variational multirateintegrators
type: conference
user_id: '47427'
year: '2014'
...
---
_id: '27426'
abstract:
- lang: eng
text: "Regularization is used in many different areas of optimization when solutions\r\nare
sought which not only minimize a given function, but also possess a certain\r\ndegree
of regularity. Popular applications are image denoising, sparse\r\nregression
and machine learning. Since the choice of the regularization\r\nparameter is crucial
but often difficult, path-following methods are used to\r\napproximate the entire
regularization path, i.e., the set of all possible\r\nsolutions for all regularization
parameters. Due to their nature, the\r\ndevelopment of these methods requires
structural results about the\r\nregularization path. The goal of this article
is to derive these results for\r\nthe case of a smooth objective function which
is penalized by a piecewise\r\ndifferentiable regularization term. We do this
by treating regularization as a\r\nmultiobjective optimization problem. Our results
suggest that even in this\r\ngeneral case, the regularization path is piecewise
smooth. Moreover, our theory\r\nallows for a classification of the nonsmooth features
that occur in between\r\nsmooth parts. This is demonstrated in two applications,
namely support-vector\r\nmachines and exact penalty methods."
author:
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Gebken B, Bieker K, Peitz S. On the structure of regularization paths for piecewise
differentiable regularization terms. Journal of Global Optimization. 2023;85(3):709-741.
doi:10.1007/s10898-022-01223-2
apa: Gebken, B., Bieker, K., & Peitz, S. (2023). On the structure of regularization
paths for piecewise differentiable regularization terms. Journal of Global
Optimization, 85(3), 709–741. https://doi.org/10.1007/s10898-022-01223-2
bibtex: '@article{Gebken_Bieker_Peitz_2023, title={On the structure of regularization
paths for piecewise differentiable regularization terms}, volume={85}, DOI={10.1007/s10898-022-01223-2},
number={3}, journal={Journal of Global Optimization}, author={Gebken, Bennet and
Bieker, Katharina and Peitz, Sebastian}, year={2023}, pages={709–741} }'
chicago: 'Gebken, Bennet, Katharina Bieker, and Sebastian Peitz. “On the Structure
of Regularization Paths for Piecewise Differentiable Regularization Terms.” Journal
of Global Optimization 85, no. 3 (2023): 709–41. https://doi.org/10.1007/s10898-022-01223-2.'
ieee: 'B. Gebken, K. Bieker, and S. Peitz, “On the structure of regularization paths
for piecewise differentiable regularization terms,” Journal of Global Optimization,
vol. 85, no. 3, pp. 709–741, 2023, doi: 10.1007/s10898-022-01223-2.'
mla: Gebken, Bennet, et al. “On the Structure of Regularization Paths for Piecewise
Differentiable Regularization Terms.” Journal of Global Optimization, vol.
85, no. 3, 2023, pp. 709–41, doi:10.1007/s10898-022-01223-2.
short: B. Gebken, K. Bieker, S. Peitz, Journal of Global Optimization 85 (2023)
709–741.
date_created: 2021-11-15T09:24:59Z
date_updated: 2023-03-11T17:16:33Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/s10898-022-01223-2
intvolume: ' 85'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://link.springer.com/content/pdf/10.1007/s10898-022-01223-2.pdf
oa: '1'
page: 709-741
publication: Journal of Global Optimization
status: public
title: On the structure of regularization paths for piecewise differentiable regularization
terms
type: journal_article
user_id: '47427'
volume: 85
year: '2023'
...
---
_id: '20731'
abstract:
- lang: eng
text: We present a novel algorithm that allows us to gain detailed insight into
the effects of sparsity in linear and nonlinear optimization, which is of great
importance in many scientific areas such as image and signal processing, medical
imaging, compressed sensing, and machine learning (e.g., for the training of neural
networks). Sparsity is an important feature to ensure robustness against noisy
data, but also to find models that are interpretable and easy to analyze due to
the small number of relevant terms. It is common practice to enforce sparsity
by adding the ℓ1-norm as a weighted penalty term. In order to gain a better understanding
and to allow for an informed model selection, we directly solve the corresponding
multiobjective optimization problem (MOP) that arises when we minimize the main
objective and the ℓ1-norm simultaneously. As this MOP is in general non-convex
for nonlinear objectives, the weighting method will fail to provide all optimal
compromises. To avoid this issue, we present a continuation method which is specifically
tailored to MOPs with two objective functions one of which is the ℓ1-norm. Our
method can be seen as a generalization of well-known homotopy methods for linear
regression problems to the nonlinear case. Several numerical examples - including
neural network training - demonstrate our theoretical findings and the additional
insight that can be gained by this multiobjective approach.
article_type: original
author:
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: Bieker K, Gebken B, Peitz S. On the Treatment of Optimization Problems with
L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions on Pattern
Analysis and Machine Intelligence. 2022;44(11):7797-7808. doi:10.1109/TPAMI.2021.3114962
apa: Bieker, K., Gebken, B., & Peitz, S. (2022). On the Treatment of Optimization
Problems with L1 Penalty Terms via Multiobjective Continuation. IEEE Transactions
on Pattern Analysis and Machine Intelligence, 44(11), 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962
bibtex: '@article{Bieker_Gebken_Peitz_2022, title={On the Treatment of Optimization
Problems with L1 Penalty Terms via Multiobjective Continuation}, volume={44},
DOI={10.1109/TPAMI.2021.3114962},
number={11}, journal={IEEE Transactions on Pattern Analysis and Machine Intelligence},
publisher={IEEE}, author={Bieker, Katharina and Gebken, Bennet and Peitz, Sebastian},
year={2022}, pages={7797–7808} }'
chicago: 'Bieker, Katharina, Bennet Gebken, and Sebastian Peitz. “On the Treatment
of Optimization Problems with L1 Penalty Terms via Multiobjective Continuation.”
IEEE Transactions on Pattern Analysis and Machine Intelligence 44, no.
11 (2022): 7797–7808. https://doi.org/10.1109/TPAMI.2021.3114962.'
ieee: 'K. Bieker, B. Gebken, and S. Peitz, “On the Treatment of Optimization Problems
with L1 Penalty Terms via Multiobjective Continuation,” IEEE Transactions on
Pattern Analysis and Machine Intelligence, vol. 44, no. 11, pp. 7797–7808,
2022, doi: 10.1109/TPAMI.2021.3114962.'
mla: Bieker, Katharina, et al. “On the Treatment of Optimization Problems with L1
Penalty Terms via Multiobjective Continuation.” IEEE Transactions on Pattern
Analysis and Machine Intelligence, vol. 44, no. 11, IEEE, 2022, pp. 7797–808,
doi:10.1109/TPAMI.2021.3114962.
short: K. Bieker, B. Gebken, S. Peitz, IEEE Transactions on Pattern Analysis and
Machine Intelligence 44 (2022) 7797–7808.
date_created: 2020-12-15T07:46:36Z
date_updated: 2022-10-21T12:27:16Z
ddc:
- '510'
department:
- _id: '101'
- _id: '530'
- _id: '655'
doi: 10.1109/TPAMI.2021.3114962
file:
- access_level: closed
content_type: application/pdf
creator: speitz
date_created: 2021-09-25T11:59:15Z
date_updated: 2021-09-25T11:59:15Z
file_id: '25040'
file_name: On_the_Treatment_of_Optimization_Problems_with_L1_Penalty_Terms_via_Multiobjective_Continuation.pdf
file_size: 7990831
relation: main_file
success: 1
file_date_updated: 2021-09-25T11:59:15Z
has_accepted_license: '1'
intvolume: ' 44'
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=9547772
oa: '1'
page: 7797-7808
publication: IEEE Transactions on Pattern Analysis and Machine Intelligence
publication_status: epub_ahead
publisher: IEEE
status: public
title: On the Treatment of Optimization Problems with L1 Penalty Terms via Multiobjective
Continuation
type: journal_article
user_id: '47427'
volume: 44
year: '2022'
...
---
_id: '21199'
abstract:
- lang: eng
text: "As in almost every other branch of science, the major advances in data\r\nscience
and machine learning have also resulted in significant improvements\r\nregarding
the modeling and simulation of nonlinear dynamical systems. It is\r\nnowadays
possible to make accurate medium to long-term predictions of highly\r\ncomplex
systems such as the weather, the dynamics within a nuclear fusion\r\nreactor,
of disease models or the stock market in a very efficient manner. In\r\nmany cases,
predictive methods are advertised to ultimately be useful for\r\ncontrol, as the
control of high-dimensional nonlinear systems is an engineering\r\ngrand challenge
with huge potential in areas such as clean and efficient energy\r\nproduction,
or the development of advanced medical devices. However, the\r\nquestion of how
to use a predictive model for control is often left unanswered\r\ndue to the associated
challenges, namely a significantly higher system\r\ncomplexity, the requirement
of much larger data sets and an increased and often\r\nproblem-specific modeling
effort. To solve these issues, we present a universal\r\nframework (which we call
QuaSiModO:\r\nQuantization-Simulation-Modeling-Optimization) to transform arbitrary\r\npredictive
models into control systems and use them for feedback control. The\r\nadvantages
of our approach are a linear increase in data requirements with\r\nrespect to
the control dimension, performance guarantees that rely exclusively\r\non the
accuracy of the predictive model, and only little prior knowledge\r\nrequirements
in control theory to solve complex control problems. In particular\r\nthe latter
point is of key importance to enable a large number of researchers\r\nand practitioners
to exploit the ever increasing capabilities of predictive\r\nmodels for control
in a straight-forward and systematic fashion."
article_number: '110840'
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
- first_name: Katharina
full_name: Bieker, Katharina
id: '32829'
last_name: Bieker
citation:
ama: Peitz S, Bieker K. On the Universal Transformation of Data-Driven Models to
Control Systems. Automatica. 2023;149. doi:10.1016/j.automatica.2022.110840
apa: Peitz, S., & Bieker, K. (2023). On the Universal Transformation of Data-Driven
Models to Control Systems. Automatica, 149, Article 110840. https://doi.org/10.1016/j.automatica.2022.110840
bibtex: '@article{Peitz_Bieker_2023, title={On the Universal Transformation of Data-Driven
Models to Control Systems}, volume={149}, DOI={10.1016/j.automatica.2022.110840},
number={110840}, journal={Automatica}, publisher={Elsevier}, author={Peitz, Sebastian
and Bieker, Katharina}, year={2023} }'
chicago: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation
of Data-Driven Models to Control Systems.” Automatica 149 (2023). https://doi.org/10.1016/j.automatica.2022.110840.
ieee: 'S. Peitz and K. Bieker, “On the Universal Transformation of Data-Driven Models
to Control Systems,” Automatica, vol. 149, Art. no. 110840, 2023, doi:
10.1016/j.automatica.2022.110840.'
mla: Peitz, Sebastian, and Katharina Bieker. “On the Universal Transformation of
Data-Driven Models to Control Systems.” Automatica, vol. 149, 110840, Elsevier,
2023, doi:10.1016/j.automatica.2022.110840.
short: S. Peitz, K. Bieker, Automatica 149 (2023).
date_created: 2021-02-10T07:04:15Z
date_updated: 2023-01-07T12:01:58Z
department:
- _id: '101'
- _id: '655'
doi: 10.1016/j.automatica.2022.110840
intvolume: ' 149'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S0005109822007075/pdfft?isDTMRedir=true&download=true
oa: '1'
project:
- _id: '52'
name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Automatica
publication_status: published
publisher: Elsevier
status: public
title: On the Universal Transformation of Data-Driven Models to Control Systems
type: journal_article
user_id: '47427'
volume: 149
year: '2023'
...
---
_id: '16596'
author:
- first_name: Kathrin
full_name: Flasskamp, Kathrin
last_name: Flasskamp
- first_name: Sina
full_name: Ober-Blobaum, Sina
last_name: Ober-Blobaum
- first_name: Tobias
full_name: Schneider, Tobias
last_name: Schneider
- first_name: Joachim
full_name: Bocker, Joachim
last_name: Bocker
citation:
ama: 'Flasskamp K, Ober-Blobaum S, Schneider T, Bocker J. Optimal control of a switched
reluctance drive by a direct method using a discrete variational principle. In:
52nd IEEE Conference on Decision and Control. ; 2014. doi:10.1109/cdc.2013.6761075'
apa: Flasskamp, K., Ober-Blobaum, S., Schneider, T., & Bocker, J. (2014). Optimal
control of a switched reluctance drive by a direct method using a discrete variational
principle. In 52nd IEEE Conference on Decision and Control. https://doi.org/10.1109/cdc.2013.6761075
bibtex: '@inproceedings{Flasskamp_Ober-Blobaum_Schneider_Bocker_2014, title={Optimal
control of a switched reluctance drive by a direct method using a discrete variational
principle}, DOI={10.1109/cdc.2013.6761075},
booktitle={52nd IEEE Conference on Decision and Control}, author={Flasskamp, Kathrin
and Ober-Blobaum, Sina and Schneider, Tobias and Bocker, Joachim}, year={2014}
}'
chicago: Flasskamp, Kathrin, Sina Ober-Blobaum, Tobias Schneider, and Joachim Bocker.
“Optimal Control of a Switched Reluctance Drive by a Direct Method Using a Discrete
Variational Principle.” In 52nd IEEE Conference on Decision and Control,
2014. https://doi.org/10.1109/cdc.2013.6761075.
ieee: K. Flasskamp, S. Ober-Blobaum, T. Schneider, and J. Bocker, “Optimal control
of a switched reluctance drive by a direct method using a discrete variational
principle,” in 52nd IEEE Conference on Decision and Control, 2014.
mla: Flasskamp, Kathrin, et al. “Optimal Control of a Switched Reluctance Drive
by a Direct Method Using a Discrete Variational Principle.” 52nd IEEE Conference
on Decision and Control, 2014, doi:10.1109/cdc.2013.6761075.
short: 'K. Flasskamp, S. Ober-Blobaum, T. Schneider, J. Bocker, in: 52nd IEEE Conference
on Decision and Control, 2014.'
date_created: 2020-04-16T05:59:29Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1109/cdc.2013.6761075
publication: 52nd IEEE Conference on Decision and Control
publication_identifier:
isbn:
- '9781467357173'
- '9781467357142'
- '9781479913817'
publication_status: published
status: public
title: Optimal control of a switched reluctance drive by a direct method using a discrete
variational principle
type: conference
user_id: '15701'
year: '2014'
...
---
_id: '16593'
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Julia
full_name: Timmermann, Julia
last_name: Timmermann
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Ansgar
full_name: Trächtler, Ansgar
last_name: Trächtler
citation:
ama: Flaßkamp K, Timmermann J, Ober-Blöbaum S, Dellnitz M, Trächtler A. Optimal
Control on Stable Manifolds for a Double Pendulum. PAMM. 2012:723-724.
doi:10.1002/pamm.201210350
apa: Flaßkamp, K., Timmermann, J., Ober-Blöbaum, S., Dellnitz, M., & Trächtler,
A. (2012). Optimal Control on Stable Manifolds for a Double Pendulum. PAMM,
723–724. https://doi.org/10.1002/pamm.201210350
bibtex: '@article{Flaßkamp_Timmermann_Ober-Blöbaum_Dellnitz_Trächtler_2012, title={Optimal
Control on Stable Manifolds for a Double Pendulum}, DOI={10.1002/pamm.201210350},
journal={PAMM}, author={Flaßkamp, Kathrin and Timmermann, Julia and Ober-Blöbaum,
Sina and Dellnitz, Michael and Trächtler, Ansgar}, year={2012}, pages={723–724}
}'
chicago: Flaßkamp, Kathrin, Julia Timmermann, Sina Ober-Blöbaum, Michael Dellnitz,
and Ansgar Trächtler. “Optimal Control on Stable Manifolds for a Double Pendulum.”
PAMM, 2012, 723–24. https://doi.org/10.1002/pamm.201210350.
ieee: K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, M. Dellnitz, and A. Trächtler,
“Optimal Control on Stable Manifolds for a Double Pendulum,” PAMM, pp.
723–724, 2012.
mla: Flaßkamp, Kathrin, et al. “Optimal Control on Stable Manifolds for a Double
Pendulum.” PAMM, 2012, pp. 723–24, doi:10.1002/pamm.201210350.
short: K. Flaßkamp, J. Timmermann, S. Ober-Blöbaum, M. Dellnitz, A. Trächtler, PAMM
(2012) 723–724.
date_created: 2020-04-16T05:54:36Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1002/pamm.201210350
language:
- iso: eng
page: 723-724
publication: PAMM
publication_identifier:
issn:
- 1617-7061
publication_status: published
status: public
title: Optimal Control on Stable Manifolds for a Double Pendulum
type: journal_article
user_id: '15701'
year: '2012'
...
---
_id: '16587'
abstract:
- lang: eng
text: We discuss nearest neighbor load balancing schemes on processor networks
which are represented by a cartesian product of graphs and present a new optimal
diffusion scheme for general graphs. In the first part of the paper, we introduce
the Alternating-Direction load balancing scheme, which reduces the number of load
balance iterations by a factor of 2 for cartesian products of graphs. The resulting
flow is theoretically analyzed and can be very high for certain cases. Therefore,
we further present the Mixed-Direction scheme which needs the same number of iterations
but computes in most cases a much smaller flow. In the second part of the paper,
we present a simple optimal diffusion scheme for general graphs, calculating a
balancing flow which is minimal in the l2 norm. It is based
on the spectra of the graph representing the network and needs only m-1 iterations
to balance the load with m being the number of distinct eigenvalues. Known optimal
diffusion schemes have the same performance, however the optimal scheme presented
in this paper can be implemented in a very simple manner. The number of iterations
of optimal diffusion schemes is independent of the load scenario and, thus, they
are practical for networks which represent graphs with known spectra. Finally,
our experiments exhibit that the new optimal scheme can successfully be combined
with the Alternating-Direction and Mixed-Direction schemes for efficient load
balancing on product graphs.
author:
- first_name: Robert
full_name: Elsässer, Robert
last_name: Elsässer
- first_name: Burkhard
full_name: Monien, Burkhard
last_name: Monien
- first_name: Robert
full_name: Preis, Robert
last_name: Preis
- first_name: Andreas
full_name: Frommer, Andreas
last_name: Frommer
citation:
ama: Elsässer R, Monien B, Preis R, Frommer A. Optimal Diffusion Schemes and Load
Balancing on Product Graphs. Parallel Processing Letters. 2004:61-73. doi:10.1142/s0129626404001714
apa: Elsässer, R., Monien, B., Preis, R., & Frommer, A. (2004). Optimal Diffusion
Schemes and Load Balancing on Product Graphs. Parallel Processing Letters,
61–73. https://doi.org/10.1142/s0129626404001714
bibtex: '@article{Elsässer_Monien_Preis_Frommer_2004, title={Optimal Diffusion Schemes
and Load Balancing on Product Graphs}, DOI={10.1142/s0129626404001714},
journal={Parallel Processing Letters}, author={Elsässer, Robert and Monien, Burkhard
and Preis, Robert and Frommer, Andreas}, year={2004}, pages={61–73} }'
chicago: Elsässer, Robert, Burkhard Monien, Robert Preis, and Andreas Frommer. “Optimal
Diffusion Schemes and Load Balancing on Product Graphs.” Parallel Processing
Letters, 2004, 61–73. https://doi.org/10.1142/s0129626404001714.
ieee: R. Elsässer, B. Monien, R. Preis, and A. Frommer, “Optimal Diffusion Schemes
and Load Balancing on Product Graphs,” Parallel Processing Letters, pp.
61–73, 2004.
mla: Elsässer, Robert, et al. “Optimal Diffusion Schemes and Load Balancing on Product
Graphs.” Parallel Processing Letters, 2004, pp. 61–73, doi:10.1142/s0129626404001714.
short: R. Elsässer, B. Monien, R. Preis, A. Frommer, Parallel Processing Letters
(2004) 61–73.
date_created: 2020-04-16T05:46:56Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1142/s0129626404001714
language:
- iso: eng
page: 61-73
publication: Parallel Processing Letters
publication_identifier:
issn:
- 0129-6264
- 1793-642X
publication_status: published
status: public
title: Optimal Diffusion Schemes and Load Balancing on Product Graphs
type: journal_article
user_id: '15701'
year: '2004'
...
---
_id: '16661'
author:
- first_name: C.
full_name: Romaus, C.
last_name: Romaus
- first_name: J.
full_name: Bocker, J.
last_name: Bocker
- first_name: K.
full_name: Witting, K.
last_name: Witting
- first_name: A.
full_name: Seifried, A.
last_name: Seifried
- first_name: O.
full_name: Znamenshchykov, O.
last_name: Znamenshchykov
citation:
ama: 'Romaus C, Bocker J, Witting K, Seifried A, Znamenshchykov O. Optimal energy
management for a hybrid energy storage system combining batteries and double layer
capacitors. In: 2009 IEEE Energy Conversion Congress and Exposition. ;
2009. doi:10.1109/ecce.2009.5316428'
apa: Romaus, C., Bocker, J., Witting, K., Seifried, A., & Znamenshchykov, O.
(2009). Optimal energy management for a hybrid energy storage system combining
batteries and double layer capacitors. In 2009 IEEE Energy Conversion Congress
and Exposition. https://doi.org/10.1109/ecce.2009.5316428
bibtex: '@inproceedings{Romaus_Bocker_Witting_Seifried_Znamenshchykov_2009, title={Optimal
energy management for a hybrid energy storage system combining batteries and double
layer capacitors}, DOI={10.1109/ecce.2009.5316428},
booktitle={2009 IEEE Energy Conversion Congress and Exposition}, author={Romaus,
C. and Bocker, J. and Witting, K. and Seifried, A. and Znamenshchykov, O.}, year={2009}
}'
chicago: Romaus, C., J. Bocker, K. Witting, A. Seifried, and O. Znamenshchykov.
“Optimal Energy Management for a Hybrid Energy Storage System Combining Batteries
and Double Layer Capacitors.” In 2009 IEEE Energy Conversion Congress and Exposition,
2009. https://doi.org/10.1109/ecce.2009.5316428.
ieee: C. Romaus, J. Bocker, K. Witting, A. Seifried, and O. Znamenshchykov, “Optimal
energy management for a hybrid energy storage system combining batteries and double
layer capacitors,” in 2009 IEEE Energy Conversion Congress and Exposition,
2009.
mla: Romaus, C., et al. “Optimal Energy Management for a Hybrid Energy Storage System
Combining Batteries and Double Layer Capacitors.” 2009 IEEE Energy Conversion
Congress and Exposition, 2009, doi:10.1109/ecce.2009.5316428.
short: 'C. Romaus, J. Bocker, K. Witting, A. Seifried, O. Znamenshchykov, in: 2009
IEEE Energy Conversion Congress and Exposition, 2009.'
date_created: 2020-04-16T09:53:32Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1109/ecce.2009.5316428
publication: 2009 IEEE Energy Conversion Congress and Exposition
publication_identifier:
isbn:
- '9781424428939'
publication_status: published
status: public
title: Optimal energy management for a hybrid energy storage system combining batteries
and double layer capacitors
type: conference
user_id: '15701'
year: '2009'
...
---
_id: '16618'
author:
- first_name: O.
full_name: Junge, O.
last_name: Junge
- first_name: S.
full_name: Ober-Blobaum, S.
last_name: Ober-Blobaum
citation:
ama: 'Junge O, Ober-Blobaum S. Optimal Reconfiguration of Formation Flying Satellites.
In: Proceedings of the 44th IEEE Conference on Decision and Control. ;
2006. doi:10.1109/cdc.2005.1582132'
apa: Junge, O., & Ober-Blobaum, S. (2006). Optimal Reconfiguration of Formation
Flying Satellites. In Proceedings of the 44th IEEE Conference on Decision and
Control. https://doi.org/10.1109/cdc.2005.1582132
bibtex: '@inproceedings{Junge_Ober-Blobaum_2006, title={Optimal Reconfiguration
of Formation Flying Satellites}, DOI={10.1109/cdc.2005.1582132},
booktitle={Proceedings of the 44th IEEE Conference on Decision and Control}, author={Junge,
O. and Ober-Blobaum, S.}, year={2006} }'
chicago: Junge, O., and S. Ober-Blobaum. “Optimal Reconfiguration of Formation Flying
Satellites.” In Proceedings of the 44th IEEE Conference on Decision and Control,
2006. https://doi.org/10.1109/cdc.2005.1582132.
ieee: O. Junge and S. Ober-Blobaum, “Optimal Reconfiguration of Formation Flying
Satellites,” in Proceedings of the 44th IEEE Conference on Decision and Control,
2006.
mla: Junge, O., and S. Ober-Blobaum. “Optimal Reconfiguration of Formation Flying
Satellites.” Proceedings of the 44th IEEE Conference on Decision and Control,
2006, doi:10.1109/cdc.2005.1582132.
short: 'O. Junge, S. Ober-Blobaum, in: Proceedings of the 44th IEEE Conference on
Decision and Control, 2006.'
date_created: 2020-04-16T08:10:25Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1109/cdc.2005.1582132
publication: Proceedings of the 44th IEEE Conference on Decision and Control
publication_identifier:
isbn:
- '0780395670'
publication_status: published
status: public
title: Optimal Reconfiguration of Formation Flying Satellites
type: conference
user_id: '15701'
year: '2006'
...
---
_id: '16621'
author:
- first_name: O.
full_name: Junge, O.
last_name: Junge
- first_name: J.E.
full_name: Marsden, J.E.
last_name: Marsden
- first_name: S.
full_name: Ober-Blobaum, S.
last_name: Ober-Blobaum
citation:
ama: 'Junge O, Marsden JE, Ober-Blobaum S. Optimal Reconfiguration of Formation
Flying Spacecraft ---a Decentralized Approach. In: Proceedings of the 45th
IEEE Conference on Decision and Control. ; 2006. doi:10.1109/cdc.2006.376977'
apa: Junge, O., Marsden, J. E., & Ober-Blobaum, S. (2006). Optimal Reconfiguration
of Formation Flying Spacecraft ---a Decentralized Approach. In Proceedings
of the 45th IEEE Conference on Decision and Control. https://doi.org/10.1109/cdc.2006.376977
bibtex: '@inproceedings{Junge_Marsden_Ober-Blobaum_2006, title={Optimal Reconfiguration
of Formation Flying Spacecraft ---a Decentralized Approach}, DOI={10.1109/cdc.2006.376977},
booktitle={Proceedings of the 45th IEEE Conference on Decision and Control}, author={Junge,
O. and Marsden, J.E. and Ober-Blobaum, S.}, year={2006} }'
chicago: Junge, O., J.E. Marsden, and S. Ober-Blobaum. “Optimal Reconfiguration
of Formation Flying Spacecraft ---a Decentralized Approach.” In Proceedings
of the 45th IEEE Conference on Decision and Control, 2006. https://doi.org/10.1109/cdc.2006.376977.
ieee: O. Junge, J. E. Marsden, and S. Ober-Blobaum, “Optimal Reconfiguration of
Formation Flying Spacecraft ---a Decentralized Approach,” in Proceedings of
the 45th IEEE Conference on Decision and Control, 2006.
mla: Junge, O., et al. “Optimal Reconfiguration of Formation Flying Spacecraft ---a
Decentralized Approach.” Proceedings of the 45th IEEE Conference on Decision
and Control, 2006, doi:10.1109/cdc.2006.376977.
short: 'O. Junge, J.E. Marsden, S. Ober-Blobaum, in: Proceedings of the 45th IEEE
Conference on Decision and Control, 2006.'
date_created: 2020-04-16T08:13:39Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1109/cdc.2006.376977
language:
- iso: eng
publication: Proceedings of the 45th IEEE Conference on Decision and Control
publication_identifier:
isbn:
- '1424401712'
publication_status: published
status: public
title: Optimal Reconfiguration of Formation Flying Spacecraft ---a Decentralized Approach
type: conference
user_id: '15701'
year: '2006'
...
---
_id: '16595'
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Todd
full_name: Murphey, Todd
last_name: Murphey
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
citation:
ama: Flaßkamp K, Murphey T, Ober-Blöbaum S. Optimization for discretized switched
systems. PAMM. 2013:401-402. doi:10.1002/pamm.201310196
apa: Flaßkamp, K., Murphey, T., & Ober-Blöbaum, S. (2013). Optimization for
discretized switched systems. PAMM, 401–402. https://doi.org/10.1002/pamm.201310196
bibtex: '@article{Flaßkamp_Murphey_Ober-Blöbaum_2013, title={Optimization for discretized
switched systems}, DOI={10.1002/pamm.201310196},
journal={PAMM}, author={Flaßkamp, Kathrin and Murphey, Todd and Ober-Blöbaum,
Sina}, year={2013}, pages={401–402} }'
chicago: Flaßkamp, Kathrin, Todd Murphey, and Sina Ober-Blöbaum. “Optimization for
Discretized Switched Systems.” PAMM, 2013, 401–2. https://doi.org/10.1002/pamm.201310196.
ieee: K. Flaßkamp, T. Murphey, and S. Ober-Blöbaum, “Optimization for discretized
switched systems,” PAMM, pp. 401–402, 2013.
mla: Flaßkamp, Kathrin, et al. “Optimization for Discretized Switched Systems.”
PAMM, 2013, pp. 401–02, doi:10.1002/pamm.201310196.
short: K. Flaßkamp, T. Murphey, S. Ober-Blöbaum, PAMM (2013) 401–402.
date_created: 2020-04-16T05:57:12Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1002/pamm.201310196
language:
- iso: eng
page: 401-402
publication: PAMM
publication_identifier:
issn:
- 1617-7061
publication_status: published
status: public
title: Optimization for discretized switched systems
type: journal_article
user_id: '15701'
year: '2013'
...
---
_id: '16629'
author:
- first_name: Martin
full_name: Krüger, Martin
last_name: Krüger
- first_name: Katrin
full_name: Witting, Katrin
last_name: Witting
- first_name: Ansgar
full_name: Trächtler, Ansgar
last_name: Trächtler
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Krüger M, Witting K, Trächtler A, Dellnitz M. Parametric Model-Order Reduction
in Hierarchical Multiobjective Optimization of Mechatronic Systems*. IFAC Proceedings
Volumes. 2011:12611-12619. doi:10.3182/20110828-6-it-1002.02487
apa: Krüger, M., Witting, K., Trächtler, A., & Dellnitz, M. (2011). Parametric
Model-Order Reduction in Hierarchical Multiobjective Optimization of Mechatronic
Systems*. IFAC Proceedings Volumes, 12611–12619. https://doi.org/10.3182/20110828-6-it-1002.02487
bibtex: '@article{Krüger_Witting_Trächtler_Dellnitz_2011, title={Parametric Model-Order
Reduction in Hierarchical Multiobjective Optimization of Mechatronic Systems*},
DOI={10.3182/20110828-6-it-1002.02487},
journal={IFAC Proceedings Volumes}, author={Krüger, Martin and Witting, Katrin
and Trächtler, Ansgar and Dellnitz, Michael}, year={2011}, pages={12611–12619}
}'
chicago: Krüger, Martin, Katrin Witting, Ansgar Trächtler, and Michael Dellnitz.
“Parametric Model-Order Reduction in Hierarchical Multiobjective Optimization
of Mechatronic Systems*.” IFAC Proceedings Volumes, 2011, 12611–19. https://doi.org/10.3182/20110828-6-it-1002.02487.
ieee: M. Krüger, K. Witting, A. Trächtler, and M. Dellnitz, “Parametric Model-Order
Reduction in Hierarchical Multiobjective Optimization of Mechatronic Systems*,”
IFAC Proceedings Volumes, pp. 12611–12619, 2011.
mla: Krüger, Martin, et al. “Parametric Model-Order Reduction in Hierarchical Multiobjective
Optimization of Mechatronic Systems*.” IFAC Proceedings Volumes, 2011,
pp. 12611–19, doi:10.3182/20110828-6-it-1002.02487.
short: M. Krüger, K. Witting, A. Trächtler, M. Dellnitz, IFAC Proceedings Volumes
(2011) 12611–12619.
date_created: 2020-04-16T08:25:21Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.3182/20110828-6-it-1002.02487
language:
- iso: eng
page: 12611-12619
publication: IFAC Proceedings Volumes
publication_identifier:
issn:
- 1474-6670
publication_status: published
status: public
title: Parametric Model-Order Reduction in Hierarchical Multiobjective Optimization
of Mechatronic Systems*
type: journal_article
user_id: '15701'
year: '2011'
...
---
_id: '10596'
abstract:
- lang: eng
text: Multi-objective optimization is an active field of research that has many
applications. Owing to its success and because decision-making processes are becoming
more and more complex, there is a recent trend for incorporating many objectives
into such problems. The challenge with such problems, however, is that the dimensions
of the solution sets—the so-called Pareto sets and fronts—grow with the number
of objectives. It is thus no longer possible to compute or to approximate the
entire solution set of a given problem that contains many (e.g. more than three)
objectives. On the other hand, the computation of single solutions (e.g. via scalarization
methods) leads to unsatisfying results in many cases, even if user preferences
are incorporated. In this article, the Pareto Explorer tool is presented—a global/local
exploration tool for the treatment of many-objective optimization problems (MaOPs).
In the first step, a solution of the problem is computed via a global search algorithm
that ideally already includes user preferences. In the second step, a local search
along the Pareto set/front of the given MaOP is performed in user specified directions.
For this, several continuation-like procedures are proposed that can incorporate
preferences defined in decision, objective, or in weight space. The applicability
and usefulness of Pareto Explorer is demonstrated on benchmark problems as well
as on an application from industrial laundry design.
article_type: original
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Oliver
full_name: Cuate, Oliver
last_name: Cuate
- first_name: Adanay
full_name: Martín, Adanay
last_name: Martín
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Schütze O, Cuate O, Martín A, Peitz S, Dellnitz M. Pareto Explorer: a global/local
exploration tool for many-objective optimization problems. Engineering Optimization.
2020;52(5):832-855. doi:10.1080/0305215x.2019.1617286'
apa: 'Schütze, O., Cuate, O., Martín, A., Peitz, S., & Dellnitz, M. (2020).
Pareto Explorer: a global/local exploration tool for many-objective optimization
problems. Engineering Optimization, 52(5), 832–855. https://doi.org/10.1080/0305215x.2019.1617286'
bibtex: '@article{Schütze_Cuate_Martín_Peitz_Dellnitz_2020, title={Pareto Explorer:
a global/local exploration tool for many-objective optimization problems}, volume={52},
DOI={10.1080/0305215x.2019.1617286},
number={5}, journal={Engineering Optimization}, author={Schütze, Oliver and Cuate,
Oliver and Martín, Adanay and Peitz, Sebastian and Dellnitz, Michael}, year={2020},
pages={832–855} }'
chicago: 'Schütze, Oliver, Oliver Cuate, Adanay Martín, Sebastian Peitz, and Michael
Dellnitz. “Pareto Explorer: A Global/Local Exploration Tool for Many-Objective
Optimization Problems.” Engineering Optimization 52, no. 5 (2020): 832–55.
https://doi.org/10.1080/0305215x.2019.1617286.'
ieee: 'O. Schütze, O. Cuate, A. Martín, S. Peitz, and M. Dellnitz, “Pareto Explorer:
a global/local exploration tool for many-objective optimization problems,” Engineering
Optimization, vol. 52, no. 5, pp. 832–855, 2020.'
mla: 'Schütze, Oliver, et al. “Pareto Explorer: A Global/Local Exploration Tool
for Many-Objective Optimization Problems.” Engineering Optimization, vol.
52, no. 5, 2020, pp. 832–55, doi:10.1080/0305215x.2019.1617286.'
short: O. Schütze, O. Cuate, A. Martín, S. Peitz, M. Dellnitz, Engineering Optimization
52 (2020) 832–855.
date_created: 2019-07-10T08:14:39Z
date_updated: 2022-01-06T06:50:46Z
department:
- _id: '101'
doi: 10.1080/0305215x.2019.1617286
intvolume: ' 52'
issue: '5'
language:
- iso: eng
page: 832-855
publication: Engineering Optimization
publication_identifier:
issn:
- 0305-215X
- 1029-0273
publication_status: published
status: public
title: 'Pareto Explorer: a global/local exploration tool for many-objective optimization
problems'
type: journal_article
user_id: '47427'
volume: 52
year: '2020'
...
---
_id: '16622'
author:
- first_name: L.
full_name: Keuck, L.
last_name: Keuck
- first_name: N.
full_name: Frohleke, N.
last_name: Frohleke
- first_name: J.
full_name: Bocker, J.
last_name: Bocker
- first_name: A.
full_name: Ziessler, A.
last_name: Ziessler
citation:
ama: 'Keuck L, Frohleke N, Bocker J, Ziessler A. PFC-control for improved inductor
utilization. In: 2015 17th European Conference on Power Electronics and Applications
(EPE’15 ECCE-Europe). ; 2015. doi:10.1109/epe.2015.7309373'
apa: Keuck, L., Frohleke, N., Bocker, J., & Ziessler, A. (2015). PFC-control
for improved inductor utilization. In 2015 17th European Conference on Power
Electronics and Applications (EPE’15 ECCE-Europe). https://doi.org/10.1109/epe.2015.7309373
bibtex: '@inproceedings{Keuck_Frohleke_Bocker_Ziessler_2015, title={PFC-control
for improved inductor utilization}, DOI={10.1109/epe.2015.7309373},
booktitle={2015 17th European Conference on Power Electronics and Applications
(EPE’15 ECCE-Europe)}, author={Keuck, L. and Frohleke, N. and Bocker, J. and Ziessler,
A.}, year={2015} }'
chicago: Keuck, L., N. Frohleke, J. Bocker, and A. Ziessler. “PFC-Control for Improved
Inductor Utilization.” In 2015 17th European Conference on Power Electronics
and Applications (EPE’15 ECCE-Europe), 2015. https://doi.org/10.1109/epe.2015.7309373.
ieee: L. Keuck, N. Frohleke, J. Bocker, and A. Ziessler, “PFC-control for improved
inductor utilization,” in 2015 17th European Conference on Power Electronics
and Applications (EPE’15 ECCE-Europe), 2015.
mla: Keuck, L., et al. “PFC-Control for Improved Inductor Utilization.” 2015
17th European Conference on Power Electronics and Applications (EPE’15 ECCE-Europe),
2015, doi:10.1109/epe.2015.7309373.
short: 'L. Keuck, N. Frohleke, J. Bocker, A. Ziessler, in: 2015 17th European Conference
on Power Electronics and Applications (EPE’15 ECCE-Europe), 2015.'
date_created: 2020-04-16T08:15:10Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1109/epe.2015.7309373
publication: 2015 17th European Conference on Power Electronics and Applications (EPE'15
ECCE-Europe)
publication_identifier:
isbn:
- '9789075815221'
publication_status: published
status: public
title: PFC-control for improved inductor utilization
type: conference
user_id: '15701'
year: '2015'
...
---
_id: '8757'
abstract:
- lang: eng
text: A framework for set‐oriented multiobjective optimal control of partial differential
equations using reduced order modeling has recently been developed [1]. Following
concepts from localized reduced bases methods, error estimators for the reduced
cost functionals are utilized to construct a library of locally valid reduced
order models. This way, a superset of the Pareto set can efficiently be computed
while maintaining a prescribed error bound. In this article, this algorithm is
applied to a problem with non‐smooth objective functionals. Using an academic
example, we show that the extension to non‐smooth problems can be realized in
a straightforward manner. We then discuss the implications on the numerical results.
author:
- first_name: Dennis
full_name: Beermann, Dennis
last_name: Beermann
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: 'Beermann D, Dellnitz M, Peitz S, Volkwein S. POD-based multiobjective optimal
control of PDEs with non-smooth objectives. In: PAMM. ; 2018:51-54. doi:10.1002/pamm.201710015'
apa: Beermann, D., Dellnitz, M., Peitz, S., & Volkwein, S. (2018). POD-based
multiobjective optimal control of PDEs with non-smooth objectives. In PAMM
(pp. 51–54). https://doi.org/10.1002/pamm.201710015
bibtex: '@inproceedings{Beermann_Dellnitz_Peitz_Volkwein_2018, title={POD-based
multiobjective optimal control of PDEs with non-smooth objectives}, DOI={10.1002/pamm.201710015},
booktitle={PAMM}, author={Beermann, Dennis and Dellnitz, Michael and Peitz, Sebastian
and Volkwein, Stefan}, year={2018}, pages={51–54} }'
chicago: Beermann, Dennis, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein.
“POD-Based Multiobjective Optimal Control of PDEs with Non-Smooth Objectives.”
In PAMM, 51–54, 2018. https://doi.org/10.1002/pamm.201710015.
ieee: D. Beermann, M. Dellnitz, S. Peitz, and S. Volkwein, “POD-based multiobjective
optimal control of PDEs with non-smooth objectives,” in PAMM, 2018, pp.
51–54.
mla: Beermann, Dennis, et al. “POD-Based Multiobjective Optimal Control of PDEs
with Non-Smooth Objectives.” PAMM, 2018, pp. 51–54, doi:10.1002/pamm.201710015.
short: 'D. Beermann, M. Dellnitz, S. Peitz, S. Volkwein, in: PAMM, 2018, pp. 51–54.'
date_created: 2019-03-29T13:34:25Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.1002/pamm.201710015
language:
- iso: eng
page: 51-54
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: PAMM
publication_identifier:
issn:
- 1617-7061
publication_status: published
status: public
title: POD-based multiobjective optimal control of PDEs with non-smooth objectives
type: conference
user_id: '47427'
year: '2018'
...
---
_id: '21943'
article_number: '244119'
author:
- first_name: Eugen
full_name: Hruska, Eugen
last_name: Hruska
- first_name: Jayvee R.
full_name: Abella, Jayvee R.
last_name: Abella
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Lydia E.
full_name: Kavraki, Lydia E.
last_name: Kavraki
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: Hruska E, Abella JR, Nüske F, Kavraki LE, Clementi C. Quantitative comparison
of adaptive sampling methods for protein dynamics. The Journal of Chemical
Physics. 2018. doi:10.1063/1.5053582
apa: Hruska, E., Abella, J. R., Nüske, F., Kavraki, L. E., & Clementi, C. (2018).
Quantitative comparison of adaptive sampling methods for protein dynamics. The
Journal of Chemical Physics. https://doi.org/10.1063/1.5053582
bibtex: '@article{Hruska_Abella_Nüske_Kavraki_Clementi_2018, title={Quantitative
comparison of adaptive sampling methods for protein dynamics}, DOI={10.1063/1.5053582},
number={244119}, journal={The Journal of Chemical Physics}, author={Hruska, Eugen
and Abella, Jayvee R. and Nüske, Feliks and Kavraki, Lydia E. and Clementi, Cecilia},
year={2018} }'
chicago: Hruska, Eugen, Jayvee R. Abella, Feliks Nüske, Lydia E. Kavraki, and Cecilia
Clementi. “Quantitative Comparison of Adaptive Sampling Methods for Protein Dynamics.”
The Journal of Chemical Physics, 2018. https://doi.org/10.1063/1.5053582.
ieee: E. Hruska, J. R. Abella, F. Nüske, L. E. Kavraki, and C. Clementi, “Quantitative
comparison of adaptive sampling methods for protein dynamics,” The Journal
of Chemical Physics, 2018.
mla: Hruska, Eugen, et al. “Quantitative Comparison of Adaptive Sampling Methods
for Protein Dynamics.” The Journal of Chemical Physics, 244119, 2018, doi:10.1063/1.5053582.
short: E. Hruska, J.R. Abella, F. Nüske, L.E. Kavraki, C. Clementi, The Journal
of Chemical Physics (2018).
date_created: 2021-04-30T17:00:24Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.5053582
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
issn:
- 0021-9606
- 1089-7690
publication_status: published
status: public
title: Quantitative comparison of adaptive sampling methods for protein dynamics
type: journal_article
user_id: '81513'
year: '2018'
...
---
_id: '21940'
author:
- first_name: Florian
full_name: Litzinger, Florian
last_name: Litzinger
- first_name: Lorenzo
full_name: Boninsegna, Lorenzo
last_name: Boninsegna
- first_name: Hao
full_name: Wu, Hao
last_name: Wu
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Raajen
full_name: Patel, Raajen
last_name: Patel
- first_name: Richard
full_name: Baraniuk, Richard
last_name: Baraniuk
- first_name: Frank
full_name: Noé, Frank
last_name: Noé
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: Litzinger F, Boninsegna L, Wu H, et al. Rapid Calculation of Molecular Kinetics
Using Compressed Sensing. Journal of Chemical Theory and Computation. 2018:2771-2783.
doi:10.1021/acs.jctc.8b00089
apa: Litzinger, F., Boninsegna, L., Wu, H., Nüske, F., Patel, R., Baraniuk, R.,
… Clementi, C. (2018). Rapid Calculation of Molecular Kinetics Using Compressed
Sensing. Journal of Chemical Theory and Computation, 2771–2783. https://doi.org/10.1021/acs.jctc.8b00089
bibtex: '@article{Litzinger_Boninsegna_Wu_Nüske_Patel_Baraniuk_Noé_Clementi_2018,
title={Rapid Calculation of Molecular Kinetics Using Compressed Sensing}, DOI={10.1021/acs.jctc.8b00089},
journal={Journal of Chemical Theory and Computation}, author={Litzinger, Florian
and Boninsegna, Lorenzo and Wu, Hao and Nüske, Feliks and Patel, Raajen and Baraniuk,
Richard and Noé, Frank and Clementi, Cecilia}, year={2018}, pages={2771–2783}
}'
chicago: Litzinger, Florian, Lorenzo Boninsegna, Hao Wu, Feliks Nüske, Raajen Patel,
Richard Baraniuk, Frank Noé, and Cecilia Clementi. “Rapid Calculation of Molecular
Kinetics Using Compressed Sensing.” Journal of Chemical Theory and Computation,
2018, 2771–83. https://doi.org/10.1021/acs.jctc.8b00089.
ieee: F. Litzinger et al., “Rapid Calculation of Molecular Kinetics Using
Compressed Sensing,” Journal of Chemical Theory and Computation, pp. 2771–2783,
2018.
mla: Litzinger, Florian, et al. “Rapid Calculation of Molecular Kinetics Using Compressed
Sensing.” Journal of Chemical Theory and Computation, 2018, pp. 2771–83,
doi:10.1021/acs.jctc.8b00089.
short: F. Litzinger, L. Boninsegna, H. Wu, F. Nüske, R. Patel, R. Baraniuk, F. Noé,
C. Clementi, Journal of Chemical Theory and Computation (2018) 2771–2783.
date_created: 2021-04-30T16:58:07Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1021/acs.jctc.8b00089
extern: '1'
language:
- iso: eng
page: 2771-2783
publication: Journal of Chemical Theory and Computation
publication_identifier:
issn:
- 1549-9618
- 1549-9626
publication_status: published
status: public
title: Rapid Calculation of Molecular Kinetics Using Compressed Sensing
type: journal_article
user_id: '81513'
year: '2018'
...
---
_id: '16660'
author:
- first_name: Maik
full_name: Ringkamp, Maik
last_name: Ringkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Sigrid
full_name: Leyendecker, Sigrid
last_name: Leyendecker
citation:
ama: Ringkamp M, Ober-Blöbaum S, Leyendecker S. Relaxing mixed integer optimal control
problems using a time transformation. PAMM. 2015:27-30. doi:10.1002/pamm.201510008
apa: Ringkamp, M., Ober-Blöbaum, S., & Leyendecker, S. (2015). Relaxing mixed
integer optimal control problems using a time transformation. PAMM, 27–30.
https://doi.org/10.1002/pamm.201510008
bibtex: '@article{Ringkamp_Ober-Blöbaum_Leyendecker_2015, title={Relaxing mixed
integer optimal control problems using a time transformation}, DOI={10.1002/pamm.201510008},
journal={PAMM}, author={Ringkamp, Maik and Ober-Blöbaum, Sina and Leyendecker,
Sigrid}, year={2015}, pages={27–30} }'
chicago: Ringkamp, Maik, Sina Ober-Blöbaum, and Sigrid Leyendecker. “Relaxing Mixed
Integer Optimal Control Problems Using a Time Transformation.” PAMM, 2015,
27–30. https://doi.org/10.1002/pamm.201510008.
ieee: M. Ringkamp, S. Ober-Blöbaum, and S. Leyendecker, “Relaxing mixed integer
optimal control problems using a time transformation,” PAMM, pp. 27–30,
2015.
mla: Ringkamp, Maik, et al. “Relaxing Mixed Integer Optimal Control Problems Using
a Time Transformation.” PAMM, 2015, pp. 27–30, doi:10.1002/pamm.201510008.
short: M. Ringkamp, S. Ober-Blöbaum, S. Leyendecker, PAMM (2015) 27–30.
date_created: 2020-04-16T09:52:20Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1002/pamm.201510008
language:
- iso: eng
page: 27-30
publication: PAMM
publication_identifier:
issn:
- 1617-7061
publication_status: published
status: public
title: Relaxing mixed integer optimal control problems using a time transformation
type: journal_article
user_id: '15701'
year: '2015'
...
---
_id: '16674'
author:
- first_name: B.
full_name: Thiere, B.
last_name: Thiere
citation:
ama: Thiere B. Return Time Dynamics as a Tool for Finding Almost Invariant Sets.
Annals of the New York Academy of Sciences. 2006:44-54. doi:10.1196/annals.1370.027
apa: Thiere, B. (2006). Return Time Dynamics as a Tool for Finding Almost Invariant
Sets. Annals of the New York Academy of Sciences, 44–54. https://doi.org/10.1196/annals.1370.027
bibtex: '@article{Thiere_2006, title={Return Time Dynamics as a Tool for Finding
Almost Invariant Sets}, DOI={10.1196/annals.1370.027},
journal={Annals of the New York Academy of Sciences}, author={Thiere, B.}, year={2006},
pages={44–54} }'
chicago: Thiere, B. “Return Time Dynamics as a Tool for Finding Almost Invariant
Sets.” Annals of the New York Academy of Sciences, 2006, 44–54. https://doi.org/10.1196/annals.1370.027.
ieee: B. Thiere, “Return Time Dynamics as a Tool for Finding Almost Invariant Sets,”
Annals of the New York Academy of Sciences, pp. 44–54, 2006.
mla: Thiere, B. “Return Time Dynamics as a Tool for Finding Almost Invariant Sets.”
Annals of the New York Academy of Sciences, 2006, pp. 44–54, doi:10.1196/annals.1370.027.
short: B. Thiere, Annals of the New York Academy of Sciences (2006) 44–54.
date_created: 2020-04-16T10:10:57Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1196/annals.1370.027
language:
- iso: eng
page: 44-54
publication: Annals of the New York Academy of Sciences
publication_identifier:
issn:
- 0077-8923
publication_status: published
status: public
title: Return Time Dynamics as a Tool for Finding Almost Invariant Sets
type: journal_article
user_id: '15701'
year: '2006'
...
---
_id: '16711'
abstract:
- lang: eng
text: "Embedding techniques allow the approximations of finite dimensional\r\nattractors
and manifolds of infinite dimensional dynamical systems via\r\nsubdivision and
continuation methods. These approximations give a topological\r\none-to-one image
of the original set. In order to additionally reveal their\r\ngeometry we use
diffusion mapst o find intrinsic coordinates. We illustrate our\r\nresults on
the unstable manifold of the one-dimensional Kuramoto--Sivashinsky\r\nequation,
as well as for the attractor of the Mackey-Glass delay differential\r\nequation."
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Gerlach R, Koltai P, Dellnitz M. Revealing the intrinsic geometry of finite
dimensional invariant sets of infinite dimensional dynamical systems. arXiv:190208824.
Published online 2019.
apa: Gerlach, R., Koltai, P., & Dellnitz, M. (2019). Revealing the intrinsic
geometry of finite dimensional invariant sets of infinite dimensional dynamical
systems. In arXiv:1902.08824.
bibtex: '@article{Gerlach_Koltai_Dellnitz_2019, title={Revealing the intrinsic geometry
of finite dimensional invariant sets of infinite dimensional dynamical systems},
journal={arXiv:1902.08824}, author={Gerlach, Raphael and Koltai, Péter and Dellnitz,
Michael}, year={2019} }'
chicago: Gerlach, Raphael, Péter Koltai, and Michael Dellnitz. “Revealing the Intrinsic
Geometry of Finite Dimensional Invariant Sets of Infinite Dimensional Dynamical
Systems.” ArXiv:1902.08824, 2019.
ieee: R. Gerlach, P. Koltai, and M. Dellnitz, “Revealing the intrinsic geometry
of finite dimensional invariant sets of infinite dimensional dynamical systems,”
arXiv:1902.08824. 2019.
mla: Gerlach, Raphael, et al. “Revealing the Intrinsic Geometry of Finite Dimensional
Invariant Sets of Infinite Dimensional Dynamical Systems.” ArXiv:1902.08824,
2019.
short: R. Gerlach, P. Koltai, M. Dellnitz, ArXiv:1902.08824 (2019).
date_created: 2020-04-16T14:06:21Z
date_updated: 2022-06-20T13:17:53Z
ddc:
- '510'
department:
- _id: '101'
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.08824
oa: '1'
publication: arXiv:1902.08824
status: public
title: Revealing the intrinsic geometry of finite dimensional invariant sets of infinite
dimensional dynamical systems
type: preprint
user_id: '32655'
year: '2019'
...
---
_id: '16601'
author:
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Gunter
full_name: Ochs, Gunter
last_name: Ochs
citation:
ama: 'Froyland G, Junge O, Ochs G. Rigorous computation of topological entropy with
respect to a finite partition. Physica D: Nonlinear Phenomena. 2001:68-84.
doi:10.1016/s0167-2789(01)00216-0'
apa: 'Froyland, G., Junge, O., & Ochs, G. (2001). Rigorous computation of topological
entropy with respect to a finite partition. Physica D: Nonlinear Phenomena,
68–84. https://doi.org/10.1016/s0167-2789(01)00216-0'
bibtex: '@article{Froyland_Junge_Ochs_2001, title={Rigorous computation of topological
entropy with respect to a finite partition}, DOI={10.1016/s0167-2789(01)00216-0},
journal={Physica D: Nonlinear Phenomena}, author={Froyland, Gary and Junge, Oliver
and Ochs, Gunter}, year={2001}, pages={68–84} }'
chicago: 'Froyland, Gary, Oliver Junge, and Gunter Ochs. “Rigorous Computation of
Topological Entropy with Respect to a Finite Partition.” Physica D: Nonlinear
Phenomena, 2001, 68–84. https://doi.org/10.1016/s0167-2789(01)00216-0.'
ieee: 'G. Froyland, O. Junge, and G. Ochs, “Rigorous computation of topological
entropy with respect to a finite partition,” Physica D: Nonlinear Phenomena,
pp. 68–84, 2001.'
mla: 'Froyland, Gary, et al. “Rigorous Computation of Topological Entropy with Respect
to a Finite Partition.” Physica D: Nonlinear Phenomena, 2001, pp. 68–84,
doi:10.1016/s0167-2789(01)00216-0.'
short: 'G. Froyland, O. Junge, G. Ochs, Physica D: Nonlinear Phenomena (2001) 68–84.'
date_created: 2020-04-16T06:08:12Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1016/s0167-2789(01)00216-0
language:
- iso: eng
page: 68-84
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
issn:
- 0167-2789
publication_status: published
status: public
title: Rigorous computation of topological entropy with respect to a finite partition
type: journal_article
user_id: '15701'
year: '2001'
...
---
_id: '16616'
author:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: 'Junge O. Rigorous discretization of subdivision techniques. In: Equadiff
99. ; 2000. doi:10.1142/9789812792617_0178'
apa: Junge, O. (2000). Rigorous discretization of subdivision techniques. In Equadiff
99. https://doi.org/10.1142/9789812792617_0178
bibtex: '@inbook{Junge_2000, title={Rigorous discretization of subdivision techniques},
DOI={10.1142/9789812792617_0178},
booktitle={Equadiff 99}, author={Junge, Oliver}, year={2000} }'
chicago: Junge, Oliver. “Rigorous Discretization of Subdivision Techniques.” In
Equadiff 99, 2000. https://doi.org/10.1142/9789812792617_0178.
ieee: O. Junge, “Rigorous discretization of subdivision techniques,” in Equadiff
99, 2000.
mla: Junge, Oliver. “Rigorous Discretization of Subdivision Techniques.” Equadiff
99, 2000, doi:10.1142/9789812792617_0178.
short: 'O. Junge, in: Equadiff 99, 2000.'
date_created: 2020-04-16T08:07:52Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1142/9789812792617_0178
language:
- iso: eng
publication: Equadiff 99
publication_identifier:
isbn:
- '9789810243593'
- '9789812792617'
publication_status: published
status: public
title: Rigorous discretization of subdivision techniques
type: book_chapter
user_id: '15701'
year: '2000'
...
---
_id: '16296'
abstract:
- lang: eng
text: "Multiobjective optimization plays an increasingly important role in modern\r\napplications,
where several objectives are often of equal importance. The task\r\nin multiobjective
optimization and multiobjective optimal control is therefore\r\nto compute the
set of optimal compromises (the Pareto set) between the\r\nconflicting objectives.
Since the Pareto set generally consists of an infinite\r\nnumber of solutions,
the computational effort can quickly become challenging\r\nwhich is particularly
problematic when the objectives are costly to evaluate as\r\nis the case for models
governed by partial differential equations (PDEs). To\r\ndecrease the numerical
effort to an affordable amount, surrogate models can be\r\nused to replace the
expensive PDE evaluations. Existing multiobjective\r\noptimization methods using
model reduction are limited either to low parameter\r\ndimensions or to few (ideally
two) objectives. In this article, we present a\r\ncombination of the reduced basis
model reduction method with a continuation\r\napproach using inexact gradients.
The resulting approach can handle an\r\narbitrary number of objectives while yielding
a significant reduction in\r\ncomputing time."
author:
- first_name: Stefan
full_name: Banholzer, Stefan
last_name: Banholzer
- first_name: Bennet
full_name: Gebken, Bennet
id: '32643'
last_name: Gebken
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: 'Banholzer S, Gebken B, Dellnitz M, Peitz S, Volkwein S. ROM-Based Multiobjective
Optimization of Elliptic PDEs via Numerical Continuation. In: Michael H, Roland
H, Christian K, Michael U, Stefan U, eds. Non-Smooth and Complementarity-Based
Distributed Parameter Systems. Springer; 2022:43-76. doi:10.1007/978-3-030-79393-7_3'
apa: Banholzer, S., Gebken, B., Dellnitz, M., Peitz, S., & Volkwein, S. (2022).
ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation.
In H. Michael, H. Roland, K. Christian, U. Michael, & U. Stefan (Eds.), Non-Smooth
and Complementarity-Based Distributed Parameter Systems (pp. 43–76). Springer.
https://doi.org/10.1007/978-3-030-79393-7_3
bibtex: '@inbook{Banholzer_Gebken_Dellnitz_Peitz_Volkwein_2022, place={Cham}, title={ROM-Based
Multiobjective Optimization of Elliptic PDEs via Numerical Continuation}, DOI={10.1007/978-3-030-79393-7_3},
booktitle={Non-Smooth and Complementarity-Based Distributed Parameter Systems},
publisher={Springer}, author={Banholzer, Stefan and Gebken, Bennet and Dellnitz,
Michael and Peitz, Sebastian and Volkwein, Stefan}, editor={Michael, Hintermüller
and Roland, Herzog and Christian, Kanzow and Michael, Ulbrich and Stefan, Ulbrich},
year={2022}, pages={43–76} }'
chicago: 'Banholzer, Stefan, Bennet Gebken, Michael Dellnitz, Sebastian Peitz, and
Stefan Volkwein. “ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical
Continuation.” In Non-Smooth and Complementarity-Based Distributed Parameter
Systems, edited by Hintermüller Michael, Herzog Roland, Kanzow Christian,
Ulbrich Michael, and Ulbrich Stefan, 43–76. Cham: Springer, 2022. https://doi.org/10.1007/978-3-030-79393-7_3.'
ieee: 'S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, and S. Volkwein, “ROM-Based
Multiobjective Optimization of Elliptic PDEs via Numerical Continuation,” in Non-Smooth
and Complementarity-Based Distributed Parameter Systems, H. Michael, H. Roland,
K. Christian, U. Michael, and U. Stefan, Eds. Cham: Springer, 2022, pp. 43–76.'
mla: Banholzer, Stefan, et al. “ROM-Based Multiobjective Optimization of Elliptic
PDEs via Numerical Continuation.” Non-Smooth and Complementarity-Based Distributed
Parameter Systems, edited by Hintermüller Michael et al., Springer, 2022,
pp. 43–76, doi:10.1007/978-3-030-79393-7_3.
short: 'S. Banholzer, B. Gebken, M. Dellnitz, S. Peitz, S. Volkwein, in: H. Michael,
H. Roland, K. Christian, U. Michael, U. Stefan (Eds.), Non-Smooth and Complementarity-Based
Distributed Parameter Systems, Springer, Cham, 2022, pp. 43–76.'
date_created: 2020-03-13T12:45:31Z
date_updated: 2022-03-14T13:04:51Z
department:
- _id: '101'
- _id: '655'
doi: 10.1007/978-3-030-79393-7_3
editor:
- first_name: Hintermüller
full_name: Michael, Hintermüller
last_name: Michael
- first_name: Herzog
full_name: Roland, Herzog
last_name: Roland
- first_name: Kanzow
full_name: Christian, Kanzow
last_name: Christian
- first_name: Ulbrich
full_name: Michael, Ulbrich
last_name: Michael
- first_name: Ulbrich
full_name: Stefan, Ulbrich
last_name: Stefan
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/pdf/1906.09075.pdf
oa: '1'
page: 43-76
place: Cham
publication: Non-Smooth and Complementarity-Based Distributed Parameter Systems
publication_identifier:
isbn:
- 978-3-030-79392-0
publisher: Springer
status: public
title: ROM-Based Multiobjective Optimization of Elliptic PDEs via Numerical Continuation
type: book_chapter
user_id: '47427'
year: '2022'
...
---
_id: '17049'
author:
- first_name: R.
full_name: Jakobsmeyer, R.
last_name: Jakobsmeyer
- first_name: R.
full_name: Schnittker, R.
last_name: Schnittker
- first_name: R.
full_name: Timmermann, R.
last_name: Timmermann
- first_name: R.
full_name: Zorn, R.
last_name: Zorn
- first_name: U.
full_name: Rückert, U.
last_name: Rückert
- first_name: J.
full_name: Baumeister, J.
last_name: Baumeister
citation:
ama: 'Jakobsmeyer R, Schnittker R, Timmermann R, Zorn R, Rückert U, Baumeister J.
Running performance analysis in basketball using recorded trajectory data. In:
Performance Analysis of Sport IX, Part 8, Routledge. ; 2013.'
apa: Jakobsmeyer, R., Schnittker, R., Timmermann, R., Zorn, R., Rückert, U., &
Baumeister, J. (2013). Running performance analysis in basketball using recorded
trajectory data. In Performance Analysis of Sport IX, Part 8, Routledge.
bibtex: '@inproceedings{Jakobsmeyer_Schnittker_Timmermann_Zorn_Rückert_Baumeister_2013,
title={Running performance analysis in basketball using recorded trajectory data},
booktitle={Performance Analysis of Sport IX, Part 8, Routledge}, author={Jakobsmeyer,
R. and Schnittker, R. and Timmermann, R. and Zorn, R. and Rückert, U. and Baumeister,
J.}, year={2013} }'
chicago: Jakobsmeyer, R., R. Schnittker, R. Timmermann, R. Zorn, U. Rückert, and
J. Baumeister. “Running Performance Analysis in Basketball Using Recorded Trajectory
Data.” In Performance Analysis of Sport IX, Part 8, Routledge, 2013.
ieee: R. Jakobsmeyer, R. Schnittker, R. Timmermann, R. Zorn, U. Rückert, and J.
Baumeister, “Running performance analysis in basketball using recorded trajectory
data,” in Performance Analysis of Sport IX, Part 8, Routledge, 2013.
mla: Jakobsmeyer, R., et al. “Running Performance Analysis in Basketball Using Recorded
Trajectory Data.” Performance Analysis of Sport IX, Part 8, Routledge,
2013.
short: 'R. Jakobsmeyer, R. Schnittker, R. Timmermann, R. Zorn, U. Rückert, J. Baumeister,
in: Performance Analysis of Sport IX, Part 8, Routledge, 2013.'
date_created: 2020-05-20T08:43:32Z
date_updated: 2022-01-06T06:53:03Z
department:
- _id: '101'
language:
- iso: eng
publication: Performance Analysis of Sport IX, Part 8, Routledge
status: public
title: Running performance analysis in basketball using recorded trajectory data
type: conference
user_id: '47427'
year: '2013'
...
---
_id: '16628'
author:
- first_name: A.
full_name: Krishnamurthy, A.
last_name: Krishnamurthy
- first_name: R.
full_name: Preis, R.
last_name: Preis
citation:
ama: 'Krishnamurthy A, Preis R. Satellite Formation, a Mobile Sensor Network in
Space. In: 19th IEEE International Parallel and Distributed Processing Symposium.
; 2005. doi:10.1109/ipdps.2005.387'
apa: Krishnamurthy, A., & Preis, R. (2005). Satellite Formation, a Mobile Sensor
Network in Space. In 19th IEEE International Parallel and Distributed Processing
Symposium. https://doi.org/10.1109/ipdps.2005.387
bibtex: '@inproceedings{Krishnamurthy_Preis_2005, title={Satellite Formation, a
Mobile Sensor Network in Space}, DOI={10.1109/ipdps.2005.387},
booktitle={19th IEEE International Parallel and Distributed Processing Symposium},
author={Krishnamurthy, A. and Preis, R.}, year={2005} }'
chicago: Krishnamurthy, A., and R. Preis. “Satellite Formation, a Mobile Sensor
Network in Space.” In 19th IEEE International Parallel and Distributed Processing
Symposium, 2005. https://doi.org/10.1109/ipdps.2005.387.
ieee: A. Krishnamurthy and R. Preis, “Satellite Formation, a Mobile Sensor Network
in Space,” in 19th IEEE International Parallel and Distributed Processing Symposium,
2005.
mla: Krishnamurthy, A., and R. Preis. “Satellite Formation, a Mobile Sensor Network
in Space.” 19th IEEE International Parallel and Distributed Processing Symposium,
2005, doi:10.1109/ipdps.2005.387.
short: 'A. Krishnamurthy, R. Preis, in: 19th IEEE International Parallel and Distributed
Processing Symposium, 2005.'
date_created: 2020-04-16T08:22:43Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1109/ipdps.2005.387
publication: 19th IEEE International Parallel and Distributed Processing Symposium
publication_identifier:
isbn:
- '0769523129'
publication_status: published
status: public
title: Satellite Formation, a Mobile Sensor Network in Space
type: conference
user_id: '15701'
year: '2005'
...
---
_id: '16573'
author:
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
- first_name: G.
full_name: Froyland, G.
last_name: Froyland
- first_name: C.
full_name: Horenkamp, C.
last_name: Horenkamp
- first_name: K.
full_name: Padberg-Gehle, K.
last_name: Padberg-Gehle
- first_name: A.
full_name: Sen Gupta, A.
last_name: Sen Gupta
citation:
ama: 'Dellnitz M, Froyland G, Horenkamp C, Padberg-Gehle K, Sen Gupta A. Seasonal
variability of the subpolar gyres in the Southern Ocean: a numerical investigation
based on transfer operators. Nonlinear Processes in Geophysics. 2009:655-663.
doi:10.5194/npg-16-655-2009'
apa: 'Dellnitz, M., Froyland, G., Horenkamp, C., Padberg-Gehle, K., & Sen Gupta,
A. (2009). Seasonal variability of the subpolar gyres in the Southern Ocean: a
numerical investigation based on transfer operators. Nonlinear Processes in
Geophysics, 655–663. https://doi.org/10.5194/npg-16-655-2009'
bibtex: '@article{Dellnitz_Froyland_Horenkamp_Padberg-Gehle_Sen Gupta_2009, title={Seasonal
variability of the subpolar gyres in the Southern Ocean: a numerical investigation
based on transfer operators}, DOI={10.5194/npg-16-655-2009},
journal={Nonlinear Processes in Geophysics}, author={Dellnitz, M. and Froyland,
G. and Horenkamp, C. and Padberg-Gehle, K. and Sen Gupta, A.}, year={2009}, pages={655–663}
}'
chicago: 'Dellnitz, M., G. Froyland, C. Horenkamp, K. Padberg-Gehle, and A. Sen
Gupta. “Seasonal Variability of the Subpolar Gyres in the Southern Ocean: A Numerical
Investigation Based on Transfer Operators.” Nonlinear Processes in Geophysics,
2009, 655–63. https://doi.org/10.5194/npg-16-655-2009.'
ieee: 'M. Dellnitz, G. Froyland, C. Horenkamp, K. Padberg-Gehle, and A. Sen Gupta,
“Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical
investigation based on transfer operators,” Nonlinear Processes in Geophysics,
pp. 655–663, 2009.'
mla: 'Dellnitz, M., et al. “Seasonal Variability of the Subpolar Gyres in the Southern
Ocean: A Numerical Investigation Based on Transfer Operators.” Nonlinear Processes
in Geophysics, 2009, pp. 655–63, doi:10.5194/npg-16-655-2009.'
short: M. Dellnitz, G. Froyland, C. Horenkamp, K. Padberg-Gehle, A. Sen Gupta, Nonlinear
Processes in Geophysics (2009) 655–663.
date_created: 2020-04-16T05:03:56Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.5194/npg-16-655-2009
language:
- iso: eng
page: 655-663
publication: Nonlinear Processes in Geophysics
publication_identifier:
issn:
- 1607-7946
publication_status: published
status: public
title: 'Seasonal variability of the subpolar gyres in the Southern Ocean: a numerical
investigation based on transfer operators'
type: journal_article
user_id: '15701'
year: '2009'
...
---
_id: '17031'
author:
- first_name: Jens
full_name: Geisler, Jens
last_name: Geisler
- first_name: Katrin
full_name: Witting, Katrin
last_name: Witting
- first_name: Ansgar
full_name: Trächtler, Ansgar
last_name: Trächtler
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Geisler J, Witting K, Trächtler A, Dellnitz M. Self-Optimization of the Guidance
Module of a Rail-bound Vehicle. In: 7th International Heinz Nixdorf Symposium:
Self-Optimizing Mechatronic Systems: Designing the Future. ; 2008.'
apa: 'Geisler, J., Witting, K., Trächtler, A., & Dellnitz, M. (2008). Self-Optimization
of the Guidance Module of a Rail-bound Vehicle. In 7th International Heinz
Nixdorf Symposium: Self-optimizing Mechatronic Systems: Designing the Future.'
bibtex: '@inproceedings{Geisler_Witting_Trächtler_Dellnitz_2008, title={Self-Optimization
of the Guidance Module of a Rail-bound Vehicle}, booktitle={7th International
Heinz Nixdorf Symposium: Self-optimizing Mechatronic Systems: Designing the Future},
author={Geisler, Jens and Witting, Katrin and Trächtler, Ansgar and Dellnitz,
Michael}, year={2008} }'
chicago: 'Geisler, Jens, Katrin Witting, Ansgar Trächtler, and Michael Dellnitz.
“Self-Optimization of the Guidance Module of a Rail-Bound Vehicle.” In 7th
International Heinz Nixdorf Symposium: Self-Optimizing Mechatronic Systems: Designing
the Future, 2008.'
ieee: 'J. Geisler, K. Witting, A. Trächtler, and M. Dellnitz, “Self-Optimization
of the Guidance Module of a Rail-bound Vehicle,” in 7th International Heinz
Nixdorf Symposium: Self-optimizing Mechatronic Systems: Designing the Future,
2008.'
mla: 'Geisler, Jens, et al. “Self-Optimization of the Guidance Module of a Rail-Bound
Vehicle.” 7th International Heinz Nixdorf Symposium: Self-Optimizing Mechatronic
Systems: Designing the Future, 2008.'
short: 'J. Geisler, K. Witting, A. Trächtler, M. Dellnitz, in: 7th International
Heinz Nixdorf Symposium: Self-Optimizing Mechatronic Systems: Designing the Future,
2008.'
date_created: 2020-05-20T07:40:22Z
date_updated: 2022-01-06T06:53:02Z
department:
- _id: '101'
language:
- iso: eng
publication: '7th International Heinz Nixdorf Symposium: Self-optimizing Mechatronic
Systems: Designing the Future'
status: public
title: Self-Optimization of the Guidance Module of a Rail-bound Vehicle
type: conference
user_id: '47427'
year: '2008'
...
---
_id: '16540'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
citation:
ama: Dellnitz M, Klus S. Sensing and control in symmetric networks. Dynamical
Systems. 2017:61-79. doi:10.1080/14689367.2016.1215410
apa: Dellnitz, M., & Klus, S. (2017). Sensing and control in symmetric networks.
Dynamical Systems, 61–79. https://doi.org/10.1080/14689367.2016.1215410
bibtex: '@article{Dellnitz_Klus_2017, title={Sensing and control in symmetric networks},
DOI={10.1080/14689367.2016.1215410},
journal={Dynamical Systems}, author={Dellnitz, Michael and Klus, Stefan}, year={2017},
pages={61–79} }'
chicago: Dellnitz, Michael, and Stefan Klus. “Sensing and Control in Symmetric Networks.”
Dynamical Systems, 2017, 61–79. https://doi.org/10.1080/14689367.2016.1215410.
ieee: M. Dellnitz and S. Klus, “Sensing and control in symmetric networks,” Dynamical
Systems, pp. 61–79, 2017.
mla: Dellnitz, Michael, and Stefan Klus. “Sensing and Control in Symmetric Networks.”
Dynamical Systems, 2017, pp. 61–79, doi:10.1080/14689367.2016.1215410.
short: M. Dellnitz, S. Klus, Dynamical Systems (2017) 61–79.
date_created: 2020-04-15T08:40:29Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1080/14689367.2016.1215410
language:
- iso: eng
page: 61-79
publication: Dynamical Systems
publication_identifier:
issn:
- 1468-9367
- 1468-9375
publication_status: published
status: public
title: Sensing and control in symmetric networks
type: journal_article
user_id: '15701'
year: '2017'
...
---
_id: '16561'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Kathrin
full_name: Padberg, Kathrin
last_name: Padberg
- first_name: Marcus
full_name: Post, Marcus
last_name: Post
- first_name: Bianca
full_name: Thiere, Bianca
last_name: Thiere
citation:
ama: 'Dellnitz M, Padberg K, Post M, Thiere B. Set Oriented Approximation of Invariant
Manifolds: Review of Concepts for Astrodynamical Problems. In: AIP Conference
Proceedings. ; 2007. doi:10.1063/1.2710046'
apa: 'Dellnitz, M., Padberg, K., Post, M., & Thiere, B. (2007). Set Oriented
Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical Problems.
In AIP Conference Proceedings. https://doi.org/10.1063/1.2710046'
bibtex: '@inproceedings{Dellnitz_Padberg_Post_Thiere_2007, title={Set Oriented Approximation
of Invariant Manifolds: Review of Concepts for Astrodynamical Problems}, DOI={10.1063/1.2710046}, booktitle={AIP
Conference Proceedings}, author={Dellnitz, Michael and Padberg, Kathrin and Post,
Marcus and Thiere, Bianca}, year={2007} }'
chicago: 'Dellnitz, Michael, Kathrin Padberg, Marcus Post, and Bianca Thiere. “Set
Oriented Approximation of Invariant Manifolds: Review of Concepts for Astrodynamical
Problems.” In AIP Conference Proceedings, 2007. https://doi.org/10.1063/1.2710046.'
ieee: 'M. Dellnitz, K. Padberg, M. Post, and B. Thiere, “Set Oriented Approximation
of Invariant Manifolds: Review of Concepts for Astrodynamical Problems,” in AIP
Conference Proceedings, 2007.'
mla: 'Dellnitz, Michael, et al. “Set Oriented Approximation of Invariant Manifolds:
Review of Concepts for Astrodynamical Problems.” AIP Conference Proceedings,
2007, doi:10.1063/1.2710046.'
short: 'M. Dellnitz, K. Padberg, M. Post, B. Thiere, in: AIP Conference Proceedings,
2007.'
date_created: 2020-04-15T10:00:16Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1063/1.2710046
publication: AIP Conference Proceedings
publication_identifier:
issn:
- 0094-243X
publication_status: published
status: public
title: 'Set Oriented Approximation of Invariant Manifolds: Review of Concepts for
Astrodynamical Problems'
type: conference
user_id: '15701'
year: '2007'
...
---
_id: '16670'
author:
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Katrin
full_name: Witting, Katrin
last_name: Witting
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: 'Schütze O, Witting K, Ober-Blöbaum S, Dellnitz M. Set Oriented Methods for
the Numerical Treatment of Multiobjective Optimization Problems. In: EVOLVE-
A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation.
Berlin, Heidelberg; 2013. doi:10.1007/978-3-642-32726-1_5'
apa: Schütze, O., Witting, K., Ober-Blöbaum, S., & Dellnitz, M. (2013). Set
Oriented Methods for the Numerical Treatment of Multiobjective Optimization Problems.
In EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary
Computation. Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32726-1_5
bibtex: '@inbook{Schütze_Witting_Ober-Blöbaum_Dellnitz_2013, place={Berlin, Heidelberg},
title={Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization
Problems}, DOI={10.1007/978-3-642-32726-1_5},
booktitle={EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary
Computation}, author={Schütze, Oliver and Witting, Katrin and Ober-Blöbaum, Sina
and Dellnitz, Michael}, year={2013} }'
chicago: Schütze, Oliver, Katrin Witting, Sina Ober-Blöbaum, and Michael Dellnitz.
“Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization
Problems.” In EVOLVE- A Bridge between Probability, Set Oriented Numerics and
Evolutionary Computation. Berlin, Heidelberg, 2013. https://doi.org/10.1007/978-3-642-32726-1_5.
ieee: O. Schütze, K. Witting, S. Ober-Blöbaum, and M. Dellnitz, “Set Oriented Methods
for the Numerical Treatment of Multiobjective Optimization Problems,” in EVOLVE-
A Bridge between Probability, Set Oriented Numerics and Evolutionary Computation,
Berlin, Heidelberg, 2013.
mla: Schütze, Oliver, et al. “Set Oriented Methods for the Numerical Treatment of
Multiobjective Optimization Problems.” EVOLVE- A Bridge between Probability,
Set Oriented Numerics and Evolutionary Computation, 2013, doi:10.1007/978-3-642-32726-1_5.
short: 'O. Schütze, K. Witting, S. Ober-Blöbaum, M. Dellnitz, in: EVOLVE- A Bridge
between Probability, Set Oriented Numerics and Evolutionary Computation, Berlin,
Heidelberg, 2013.'
date_created: 2020-04-16T10:05:59Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/978-3-642-32726-1_5
language:
- iso: eng
place: Berlin, Heidelberg
publication: EVOLVE- A Bridge between Probability, Set Oriented Numerics and Evolutionary
Computation
publication_identifier:
isbn:
- '9783642327254'
- '9783642327261'
issn:
- 1860-949X
- 1860-9503
publication_status: published
status: public
title: Set Oriented Methods for the Numerical Treatment of Multiobjective Optimization
Problems
type: book_chapter
user_id: '15701'
year: '2013'
...
---
_id: '16538'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: 'Dellnitz M, Junge O. Set Oriented Numerical Methods for Dynamical Systems.
In: Handbook of Dynamical Systems. ; 2002. doi:10.1016/s1874-575x(02)80026-1'
apa: Dellnitz, M., & Junge, O. (2002). Set Oriented Numerical Methods for Dynamical
Systems. In Handbook of Dynamical Systems. https://doi.org/10.1016/s1874-575x(02)80026-1
bibtex: '@inbook{Dellnitz_Junge_2002, title={Set Oriented Numerical Methods for
Dynamical Systems}, DOI={10.1016/s1874-575x(02)80026-1},
booktitle={Handbook of Dynamical Systems}, author={Dellnitz, Michael and Junge,
Oliver}, year={2002} }'
chicago: Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods for
Dynamical Systems.” In Handbook of Dynamical Systems, 2002. https://doi.org/10.1016/s1874-575x(02)80026-1.
ieee: M. Dellnitz and O. Junge, “Set Oriented Numerical Methods for Dynamical Systems,”
in Handbook of Dynamical Systems, 2002.
mla: Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods for Dynamical
Systems.” Handbook of Dynamical Systems, 2002, doi:10.1016/s1874-575x(02)80026-1.
short: 'M. Dellnitz, O. Junge, in: Handbook of Dynamical Systems, 2002.'
date_created: 2020-04-15T08:37:59Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1016/s1874-575x(02)80026-1
language:
- iso: eng
publication: Handbook of Dynamical Systems
publication_identifier:
isbn:
- '9780444501684'
issn:
- 1874-575X
publication_status: published
status: public
title: Set Oriented Numerical Methods for Dynamical Systems
type: book_chapter
user_id: '15701'
year: '2002'
...
---
_id: '16539'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: 'Dellnitz M, Junge O. Set Oriented Numerical Methods in Space Mission Design.
In: Elsevier Astrodynamics Series. ; 2006. doi:10.1016/s1874-9305(07)80007-0'
apa: Dellnitz, M., & Junge, O. (2006). Set Oriented Numerical Methods in Space
Mission Design. In Elsevier Astrodynamics Series. https://doi.org/10.1016/s1874-9305(07)80007-0
bibtex: '@inbook{Dellnitz_Junge_2006, title={Set Oriented Numerical Methods in Space
Mission Design}, DOI={10.1016/s1874-9305(07)80007-0},
booktitle={Elsevier Astrodynamics Series}, author={Dellnitz, Michael and Junge,
Oliver}, year={2006} }'
chicago: Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods in
Space Mission Design.” In Elsevier Astrodynamics Series, 2006. https://doi.org/10.1016/s1874-9305(07)80007-0.
ieee: M. Dellnitz and O. Junge, “Set Oriented Numerical Methods in Space Mission
Design,” in Elsevier Astrodynamics Series, 2006.
mla: Dellnitz, Michael, and Oliver Junge. “Set Oriented Numerical Methods in Space
Mission Design.” Elsevier Astrodynamics Series, 2006, doi:10.1016/s1874-9305(07)80007-0.
short: 'M. Dellnitz, O. Junge, in: Elsevier Astrodynamics Series, 2006.'
date_created: 2020-04-15T08:39:13Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1016/s1874-9305(07)80007-0
language:
- iso: eng
publication: Elsevier Astrodynamics Series
publication_identifier:
isbn:
- '9780123735621'
issn:
- 1874-9305
publication_status: published
status: public
title: Set Oriented Numerical Methods in Space Mission Design
type: book_chapter
user_id: '15701'
year: '2006'
...
---
_id: '8754'
abstract:
- lang: eng
text: In this chapter, we combine a global, derivative-free subdivision algorithm
for multiobjective optimization problems with a posteriori error estimates for
reduced-order models based on Proper Orthogonal Decomposition in order to efficiently
solve multiobjective optimization problems governed by partial differential equations.
An error bound for a semilinear heat equation is developed in such a way that
the errors in the conflicting objectives can be estimated individually. The resulting
algorithm constructs a library of locally valid reduced-order models online using
a Greedy (worst-first) search. Using this approach, the number of evaluations
of the full-order model can be reduced by a factor of more than 1000.
author:
- first_name: Dennis
full_name: Beermann, Dennis
last_name: Beermann
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Stefan
full_name: Volkwein, Stefan
last_name: Volkwein
citation:
ama: 'Beermann D, Dellnitz M, Peitz S, Volkwein S. Set-Oriented Multiobjective Optimal
Control of PDEs Using Proper Orthogonal Decomposition. In: Reduced-Order Modeling
(ROM) for Simulation and Optimization. Cham; 2018:47-72. doi:10.1007/978-3-319-75319-5_3'
apa: Beermann, D., Dellnitz, M., Peitz, S., & Volkwein, S. (2018). Set-Oriented
Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition.
In Reduced-Order Modeling (ROM) for Simulation and Optimization (pp. 47–72).
Cham. https://doi.org/10.1007/978-3-319-75319-5_3
bibtex: '@inbook{Beermann_Dellnitz_Peitz_Volkwein_2018, place={Cham}, title={Set-Oriented
Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition},
DOI={10.1007/978-3-319-75319-5_3},
booktitle={Reduced-Order Modeling (ROM) for Simulation and Optimization}, author={Beermann,
Dennis and Dellnitz, Michael and Peitz, Sebastian and Volkwein, Stefan}, year={2018},
pages={47–72} }'
chicago: Beermann, Dennis, Michael Dellnitz, Sebastian Peitz, and Stefan Volkwein.
“Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal Decomposition.”
In Reduced-Order Modeling (ROM) for Simulation and Optimization, 47–72.
Cham, 2018. https://doi.org/10.1007/978-3-319-75319-5_3.
ieee: D. Beermann, M. Dellnitz, S. Peitz, and S. Volkwein, “Set-Oriented Multiobjective
Optimal Control of PDEs Using Proper Orthogonal Decomposition,” in Reduced-Order
Modeling (ROM) for Simulation and Optimization, Cham, 2018, pp. 47–72.
mla: Beermann, Dennis, et al. “Set-Oriented Multiobjective Optimal Control of PDEs
Using Proper Orthogonal Decomposition.” Reduced-Order Modeling (ROM) for Simulation
and Optimization, 2018, pp. 47–72, doi:10.1007/978-3-319-75319-5_3.
short: 'D. Beermann, M. Dellnitz, S. Peitz, S. Volkwein, in: Reduced-Order Modeling
(ROM) for Simulation and Optimization, Cham, 2018, pp. 47–72.'
date_created: 2019-03-29T13:31:20Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.1007/978-3-319-75319-5_3
language:
- iso: eng
page: 47-72
place: Cham
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Reduced-Order Modeling (ROM) for Simulation and Optimization
publication_identifier:
isbn:
- '9783319753188'
- '9783319753195'
publication_status: published
status: public
title: Set-Oriented Multiobjective Optimal Control of PDEs Using Proper Orthogonal
Decomposition
type: book_chapter
user_id: '47427'
year: '2018'
...
---
_id: '16592'
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Marin
full_name: Kobilarov, Marin
last_name: Kobilarov
citation:
ama: Flaßkamp K, Ober-Blöbaum S, Kobilarov M. Solving Optimal Control Problems by
Exploiting Inherent Dynamical Systems Structures. Journal of Nonlinear Science.
2012:599-629. doi:10.1007/s00332-012-9140-7
apa: Flaßkamp, K., Ober-Blöbaum, S., & Kobilarov, M. (2012). Solving Optimal
Control Problems by Exploiting Inherent Dynamical Systems Structures. Journal
of Nonlinear Science, 599–629. https://doi.org/10.1007/s00332-012-9140-7
bibtex: '@article{Flaßkamp_Ober-Blöbaum_Kobilarov_2012, title={Solving Optimal Control
Problems by Exploiting Inherent Dynamical Systems Structures}, DOI={10.1007/s00332-012-9140-7},
journal={Journal of Nonlinear Science}, author={Flaßkamp, Kathrin and Ober-Blöbaum,
Sina and Kobilarov, Marin}, year={2012}, pages={599–629} }'
chicago: Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Marin Kobilarov. “Solving Optimal
Control Problems by Exploiting Inherent Dynamical Systems Structures.” Journal
of Nonlinear Science, 2012, 599–629. https://doi.org/10.1007/s00332-012-9140-7.
ieee: K. Flaßkamp, S. Ober-Blöbaum, and M. Kobilarov, “Solving Optimal Control Problems
by Exploiting Inherent Dynamical Systems Structures,” Journal of Nonlinear
Science, pp. 599–629, 2012.
mla: Flaßkamp, Kathrin, et al. “Solving Optimal Control Problems by Exploiting Inherent
Dynamical Systems Structures.” Journal of Nonlinear Science, 2012, pp.
599–629, doi:10.1007/s00332-012-9140-7.
short: K. Flaßkamp, S. Ober-Blöbaum, M. Kobilarov, Journal of Nonlinear Science
(2012) 599–629.
date_created: 2020-04-16T05:53:07Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/s00332-012-9140-7
language:
- iso: eng
page: 599-629
publication: Journal of Nonlinear Science
publication_identifier:
issn:
- 0938-8974
- 1432-1467
publication_status: published
status: public
title: Solving Optimal Control Problems by Exploiting Inherent Dynamical Systems Structures
type: journal_article
user_id: '15701'
year: '2012'
...
---
_id: '16590'
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Marin
full_name: Kobilarov, Marin
last_name: Kobilarov
citation:
ama: Flaßkamp K, Ober-Blöbaum S, Kobilarov M. Solving optimal control problems by
using inherent dynamical properties. PAMM. 2010:577-578. doi:10.1002/pamm.201010281
apa: Flaßkamp, K., Ober-Blöbaum, S., & Kobilarov, M. (2010). Solving optimal
control problems by using inherent dynamical properties. PAMM, 577–578.
https://doi.org/10.1002/pamm.201010281
bibtex: '@article{Flaßkamp_Ober-Blöbaum_Kobilarov_2010, title={Solving optimal control
problems by using inherent dynamical properties}, DOI={10.1002/pamm.201010281},
journal={PAMM}, author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Kobilarov,
Marin}, year={2010}, pages={577–578} }'
chicago: Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Marin Kobilarov. “Solving Optimal
Control Problems by Using Inherent Dynamical Properties.” PAMM, 2010, 577–78.
https://doi.org/10.1002/pamm.201010281.
ieee: K. Flaßkamp, S. Ober-Blöbaum, and M. Kobilarov, “Solving optimal control problems
by using inherent dynamical properties,” PAMM, pp. 577–578, 2010.
mla: Flaßkamp, Kathrin, et al. “Solving Optimal Control Problems by Using Inherent
Dynamical Properties.” PAMM, 2010, pp. 577–78, doi:10.1002/pamm.201010281.
short: K. Flaßkamp, S. Ober-Blöbaum, M. Kobilarov, PAMM (2010) 577–578.
date_created: 2020-04-16T05:50:45Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1002/pamm.201010281
language:
- iso: eng
page: 577-578
publication: PAMM
publication_identifier:
issn:
- 1617-7061
publication_status: published
status: public
title: Solving optimal control problems by using inherent dynamical properties
type: journal_article
user_id: '15701'
year: '2010'
...
---
_id: '16673'
author:
- first_name: Marco
full_name: Tantardini, Marco
last_name: Tantardini
- first_name: Elena
full_name: Fantino, Elena
last_name: Fantino
- first_name: Yuan
full_name: Ren, Yuan
last_name: Ren
- first_name: Pierpaolo
full_name: Pergola, Pierpaolo
last_name: Pergola
- first_name: Gerard
full_name: Gómez, Gerard
last_name: Gómez
- first_name: Josep J.
full_name: Masdemont, Josep J.
last_name: Masdemont
citation:
ama: Tantardini M, Fantino E, Ren Y, Pergola P, Gómez G, Masdemont JJ. Spacecraft
trajectories to the L3 point of the Sun–Earth three-body problem. Celestial
Mechanics and Dynamical Astronomy. 2010:215-232. doi:10.1007/s10569-010-9299-x
apa: Tantardini, M., Fantino, E., Ren, Y., Pergola, P., Gómez, G., & Masdemont,
J. J. (2010). Spacecraft trajectories to the L3 point of the Sun–Earth three-body
problem. Celestial Mechanics and Dynamical Astronomy, 215–232. https://doi.org/10.1007/s10569-010-9299-x
bibtex: '@article{Tantardini_Fantino_Ren_Pergola_Gómez_Masdemont_2010, title={Spacecraft
trajectories to the L3 point of the Sun–Earth three-body problem}, DOI={10.1007/s10569-010-9299-x},
journal={Celestial Mechanics and Dynamical Astronomy}, author={Tantardini, Marco
and Fantino, Elena and Ren, Yuan and Pergola, Pierpaolo and Gómez, Gerard and
Masdemont, Josep J.}, year={2010}, pages={215–232} }'
chicago: Tantardini, Marco, Elena Fantino, Yuan Ren, Pierpaolo Pergola, Gerard Gómez,
and Josep J. Masdemont. “Spacecraft Trajectories to the L3 Point of the Sun–Earth
Three-Body Problem.” Celestial Mechanics and Dynamical Astronomy, 2010,
215–32. https://doi.org/10.1007/s10569-010-9299-x.
ieee: M. Tantardini, E. Fantino, Y. Ren, P. Pergola, G. Gómez, and J. J. Masdemont,
“Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem,”
Celestial Mechanics and Dynamical Astronomy, pp. 215–232, 2010.
mla: Tantardini, Marco, et al. “Spacecraft Trajectories to the L3 Point of the Sun–Earth
Three-Body Problem.” Celestial Mechanics and Dynamical Astronomy, 2010,
pp. 215–32, doi:10.1007/s10569-010-9299-x.
short: M. Tantardini, E. Fantino, Y. Ren, P. Pergola, G. Gómez, J.J. Masdemont,
Celestial Mechanics and Dynamical Astronomy (2010) 215–232.
date_created: 2020-04-16T10:09:58Z
date_updated: 2022-01-06T06:52:54Z
department:
- _id: '101'
doi: 10.1007/s10569-010-9299-x
language:
- iso: eng
page: 215-232
publication: Celestial Mechanics and Dynamical Astronomy
publication_identifier:
issn:
- 0923-2958
- 1572-9478
publication_status: published
status: public
title: Spacecraft trajectories to the L3 point of the Sun–Earth three-body problem
type: journal_article
user_id: '15701'
year: '2010'
...
---
_id: '21942'
article_number: '241723'
author:
- first_name: Lorenzo
full_name: Boninsegna, Lorenzo
last_name: Boninsegna
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: Boninsegna L, Nüske F, Clementi C. Sparse learning of stochastic dynamical
equations. The Journal of Chemical Physics. 2018. doi:10.1063/1.5018409
apa: Boninsegna, L., Nüske, F., & Clementi, C. (2018). Sparse learning of stochastic
dynamical equations. The Journal of Chemical Physics. https://doi.org/10.1063/1.5018409
bibtex: '@article{Boninsegna_Nüske_Clementi_2018, title={Sparse learning of stochastic
dynamical equations}, DOI={10.1063/1.5018409},
number={241723}, journal={The Journal of Chemical Physics}, author={Boninsegna,
Lorenzo and Nüske, Feliks and Clementi, Cecilia}, year={2018} }'
chicago: Boninsegna, Lorenzo, Feliks Nüske, and Cecilia Clementi. “Sparse Learning
of Stochastic Dynamical Equations.” The Journal of Chemical Physics, 2018.
https://doi.org/10.1063/1.5018409.
ieee: L. Boninsegna, F. Nüske, and C. Clementi, “Sparse learning of stochastic dynamical
equations,” The Journal of Chemical Physics, 2018.
mla: Boninsegna, Lorenzo, et al. “Sparse Learning of Stochastic Dynamical Equations.”
The Journal of Chemical Physics, 241723, 2018, doi:10.1063/1.5018409.
short: L. Boninsegna, F. Nüske, C. Clementi, The Journal of Chemical Physics (2018).
date_created: 2021-04-30T16:59:39Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.5018409
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
issn:
- 0021-9606
- 1089-7690
publication_status: published
status: public
title: Sparse learning of stochastic dynamical equations
type: journal_article
user_id: '81513'
year: '2018'
...
---
_id: '21820'
abstract:
- lang: eng
text: The reduction of high-dimensional systems to effective models on a
smaller set of variables is an essential task in many areas of science. For stochastic
dynamics governed by diffusion processes, a general procedure to find effective
equations is the conditioning approach. In this paper, we are interested in the
spectrum of the generator of the resulting effective dynamics, and how it compares
to the spectrum of the full generator. We prove a new relative error bound in
terms of the eigenfunction approximation error for reversible systems. We also
present numerical examples indicating that, if Kramers–Moyal (KM) type approximations
are used to compute the spectrum of the reduced generator, it seems largely insensitive
to the time window used for the KM estimators. We analyze the implications of
these observations for systems driven by underdamped Langevin dynamics, and show
how meaningful effective dynamics can be defined in this setting.
article_number: '134'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
- first_name: Lorenzo
full_name: Boninsegna, Lorenzo
last_name: Boninsegna
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: Nüske F, Koltai P, Boninsegna L, Clementi C. Spectral Properties of Effective
Dynamics from Conditional Expectations. Entropy. 2021. doi:10.3390/e23020134
apa: Nüske, F., Koltai, P., Boninsegna, L., & Clementi, C. (2021). Spectral
Properties of Effective Dynamics from Conditional Expectations. Entropy.
https://doi.org/10.3390/e23020134
bibtex: '@article{Nüske_Koltai_Boninsegna_Clementi_2021, title={Spectral Properties
of Effective Dynamics from Conditional Expectations}, DOI={10.3390/e23020134},
number={134}, journal={Entropy}, author={Nüske, Feliks and Koltai, Péter and Boninsegna,
Lorenzo and Clementi, Cecilia}, year={2021} }'
chicago: Nüske, Feliks, Péter Koltai, Lorenzo Boninsegna, and Cecilia Clementi.
“Spectral Properties of Effective Dynamics from Conditional Expectations.” Entropy,
2021. https://doi.org/10.3390/e23020134.
ieee: F. Nüske, P. Koltai, L. Boninsegna, and C. Clementi, “Spectral Properties
of Effective Dynamics from Conditional Expectations,” Entropy, 2021.
mla: Nüske, Feliks, et al. “Spectral Properties of Effective Dynamics from Conditional
Expectations.” Entropy, 134, 2021, doi:10.3390/e23020134.
short: F. Nüske, P. Koltai, L. Boninsegna, C. Clementi, Entropy (2021).
date_created: 2021-04-28T18:07:56Z
date_updated: 2022-01-06T06:55:16Z
department:
- _id: '101'
doi: 10.3390/e23020134
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.mdpi.com/1099-4300/23/2/134
oa: '1'
publication: Entropy
publication_identifier:
issn:
- 1099-4300
publication_status: published
status: public
title: Spectral Properties of Effective Dynamics from Conditional Expectations
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '17028'
author:
- first_name: Massimiliano
full_name: Vasile, Massimiliano
last_name: Vasile
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Gimbardo
full_name: Radice, Gimbardo
last_name: Radice
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Vasile M, Schütze O, Junge O, Radice G, Dellnitz M. Spiral Trajectories
in Global Optimisation of Interplanetary and Orbital Transfers. European Space
Agency; 2007.
apa: Vasile, M., Schütze, O., Junge, O., Radice, G., & Dellnitz, M. (2007).
Spiral Trajectories in Global Optimisation of Interplanetary and Orbital Transfers.
European Space Agency.
bibtex: '@book{Vasile_Schütze_Junge_Radice_Dellnitz_2007, title={Spiral Trajectories
in Global Optimisation of Interplanetary and Orbital Transfers}, publisher={European
Space Agency}, author={Vasile, Massimiliano and Schütze, Oliver and Junge, Oliver
and Radice, Gimbardo and Dellnitz, Michael}, year={2007} }'
chicago: Vasile, Massimiliano, Oliver Schütze, Oliver Junge, Gimbardo Radice, and
Michael Dellnitz. Spiral Trajectories in Global Optimisation of Interplanetary
and Orbital Transfers. European Space Agency, 2007.
ieee: M. Vasile, O. Schütze, O. Junge, G. Radice, and M. Dellnitz, Spiral Trajectories
in Global Optimisation of Interplanetary and Orbital Transfers. European Space
Agency, 2007.
mla: Vasile, Massimiliano, et al. Spiral Trajectories in Global Optimisation
of Interplanetary and Orbital Transfers. European Space Agency, 2007.
short: M. Vasile, O. Schütze, O. Junge, G. Radice, M. Dellnitz, Spiral Trajectories
in Global Optimisation of Interplanetary and Orbital Transfers, European Space
Agency, 2007.
date_created: 2020-05-20T07:30:07Z
date_updated: 2022-01-06T06:53:02Z
department:
- _id: '101'
language:
- iso: eng
publisher: European Space Agency
report_number: AO 05/4106
status: public
title: Spiral Trajectories in Global Optimisation of Interplanetary and Orbital Transfers
type: report
user_id: '47427'
year: '2007'
...
---
_id: '16551'
abstract:
- lang: eng
text: Spiral patterns have been observed experimentally, numerically, and
theoretically in a variety of systems. It is often believed that these spiral
wave patterns can occur only in systems of reaction–diffusion equations. We show,
both theoretically (using Hopf bifurcation techniques) and numerically (using
both direct simulation and continuation of rotating waves) that spiral wave patterns
can appear in a single reaction–diffusion equation [ in u(x, t)] on a disk, if
one assumes "spiral" boundary conditions (ur = muθ).
Spiral boundary conditions are motivated by assuming that a solution is infinitesimally
an Archimedian spiral near the boundary. It follows from a bifurcation analysis
that for this form of spirals there are no singularities in the spiral pattern
(technically there is no spiral tip) and that at bifurcation there is a steep
gradient between the "red" and "blue" arms of the spiral.
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Martin
full_name: Golubitsky, Martin
last_name: Golubitsky
- first_name: Andreas
full_name: Hohmann, Andreas
last_name: Hohmann
- first_name: Ian
full_name: Stewart, Ian
last_name: Stewart
citation:
ama: Dellnitz M, Golubitsky M, Hohmann A, Stewart I. Spirals in Scalar Reaction–Diffusion
Equations. International Journal of Bifurcation and Chaos. 1995:1487-1501.
doi:10.1142/s0218127495001149
apa: Dellnitz, M., Golubitsky, M., Hohmann, A., & Stewart, I. (1995). Spirals
in Scalar Reaction–Diffusion Equations. International Journal of Bifurcation
and Chaos, 1487–1501. https://doi.org/10.1142/s0218127495001149
bibtex: '@article{Dellnitz_Golubitsky_Hohmann_Stewart_1995, title={Spirals in Scalar
Reaction–Diffusion Equations}, DOI={10.1142/s0218127495001149},
journal={International Journal of Bifurcation and Chaos}, author={Dellnitz, Michael
and Golubitsky, Martin and Hohmann, Andreas and Stewart, Ian}, year={1995}, pages={1487–1501}
}'
chicago: Dellnitz, Michael, Martin Golubitsky, Andreas Hohmann, and Ian Stewart.
“Spirals in Scalar Reaction–Diffusion Equations.” International Journal of
Bifurcation and Chaos, 1995, 1487–1501. https://doi.org/10.1142/s0218127495001149.
ieee: M. Dellnitz, M. Golubitsky, A. Hohmann, and I. Stewart, “Spirals in Scalar
Reaction–Diffusion Equations,” International Journal of Bifurcation and Chaos,
pp. 1487–1501, 1995.
mla: Dellnitz, Michael, et al. “Spirals in Scalar Reaction–Diffusion Equations.”
International Journal of Bifurcation and Chaos, 1995, pp. 1487–501, doi:10.1142/s0218127495001149.
short: M. Dellnitz, M. Golubitsky, A. Hohmann, I. Stewart, International Journal
of Bifurcation and Chaos (1995) 1487–1501.
date_created: 2020-04-15T09:05:30Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1142/s0218127495001149
language:
- iso: eng
page: 1487-1501
publication: International Journal of Bifurcation and Chaos
publication_identifier:
issn:
- 0218-1274
- 1793-6551
publication_status: published
status: public
title: Spirals in Scalar Reaction–Diffusion Equations
type: journal_article
user_id: '15701'
year: '1995'
...
---
_id: '17034'
author:
- first_name: Sebastian
full_name: Hage-Packhäuser, Sebastian
last_name: Hage-Packhäuser
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Hage-Packhäuser S, Dellnitz M. Stabilization via symmetry switching in hybrid
dynamical systems. Discrete & Continuous Dynamical Systems - B. 2011;16(1):239-263.
doi:10.3934/dcdsb.2011.16.239
apa: Hage-Packhäuser, S., & Dellnitz, M. (2011). Stabilization via symmetry
switching in hybrid dynamical systems. Discrete & Continuous Dynamical
Systems - B, 16(1), 239–263. https://doi.org/10.3934/dcdsb.2011.16.239
bibtex: '@article{Hage-Packhäuser_Dellnitz_2011, title={Stabilization via symmetry
switching in hybrid dynamical systems}, volume={16}, DOI={10.3934/dcdsb.2011.16.239},
number={1}, journal={Discrete & Continuous Dynamical Systems - B}, author={Hage-Packhäuser,
Sebastian and Dellnitz, Michael}, year={2011}, pages={239–263} }'
chicago: 'Hage-Packhäuser, Sebastian, and Michael Dellnitz. “Stabilization via Symmetry
Switching in Hybrid Dynamical Systems.” Discrete & Continuous Dynamical
Systems - B 16, no. 1 (2011): 239–63. https://doi.org/10.3934/dcdsb.2011.16.239.'
ieee: S. Hage-Packhäuser and M. Dellnitz, “Stabilization via symmetry switching
in hybrid dynamical systems,” Discrete & Continuous Dynamical Systems -
B, vol. 16, no. 1, pp. 239–263, 2011.
mla: Hage-Packhäuser, Sebastian, and Michael Dellnitz. “Stabilization via Symmetry
Switching in Hybrid Dynamical Systems.” Discrete & Continuous Dynamical
Systems - B, vol. 16, no. 1, 2011, pp. 239–63, doi:10.3934/dcdsb.2011.16.239.
short: S. Hage-Packhäuser, M. Dellnitz, Discrete & Continuous Dynamical Systems
- B 16 (2011) 239–263.
date_created: 2020-05-20T07:56:34Z
date_updated: 2022-01-06T06:53:02Z
department:
- _id: '101'
doi: 10.3934/dcdsb.2011.16.239
intvolume: ' 16'
issue: '1'
language:
- iso: eng
page: 239-263
publication: Discrete & Continuous Dynamical Systems - B
status: public
title: Stabilization via symmetry switching in hybrid dynamical systems
type: journal_article
user_id: '47427'
volume: 16
year: '2011'
...
---
_id: '16591'
author:
- first_name: Kathrin
full_name: Flasskamp, Kathrin
last_name: Flasskamp
- first_name: Todd
full_name: Murphey, Todd
last_name: Murphey
- first_name: Sina
full_name: Ober-Blobaum, Sina
last_name: Ober-Blobaum
citation:
ama: 'Flasskamp K, Murphey T, Ober-Blobaum S. Switching time optimization in discretized
hybrid dynamical systems. In: 2012 IEEE 51st IEEE Conference on Decision and
Control (CDC). ; 2012. doi:10.1109/cdc.2012.6426414'
apa: Flasskamp, K., Murphey, T., & Ober-Blobaum, S. (2012). Switching time optimization
in discretized hybrid dynamical systems. In 2012 IEEE 51st IEEE Conference
on Decision and Control (CDC). https://doi.org/10.1109/cdc.2012.6426414
bibtex: '@inproceedings{Flasskamp_Murphey_Ober-Blobaum_2012, title={Switching time
optimization in discretized hybrid dynamical systems}, DOI={10.1109/cdc.2012.6426414},
booktitle={2012 IEEE 51st IEEE Conference on Decision and Control (CDC)}, author={Flasskamp,
Kathrin and Murphey, Todd and Ober-Blobaum, Sina}, year={2012} }'
chicago: Flasskamp, Kathrin, Todd Murphey, and Sina Ober-Blobaum. “Switching Time
Optimization in Discretized Hybrid Dynamical Systems.” In 2012 IEEE 51st IEEE
Conference on Decision and Control (CDC), 2012. https://doi.org/10.1109/cdc.2012.6426414.
ieee: K. Flasskamp, T. Murphey, and S. Ober-Blobaum, “Switching time optimization
in discretized hybrid dynamical systems,” in 2012 IEEE 51st IEEE Conference
on Decision and Control (CDC), 2012.
mla: Flasskamp, Kathrin, et al. “Switching Time Optimization in Discretized Hybrid
Dynamical Systems.” 2012 IEEE 51st IEEE Conference on Decision and Control
(CDC), 2012, doi:10.1109/cdc.2012.6426414.
short: 'K. Flasskamp, T. Murphey, S. Ober-Blobaum, in: 2012 IEEE 51st IEEE Conference
on Decision and Control (CDC), 2012.'
date_created: 2020-04-16T05:51:38Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1109/cdc.2012.6426414
language:
- iso: eng
publication: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC)
publication_identifier:
isbn:
- '9781467320665'
- '9781467320658'
- '9781467320634'
- '9781467320641'
publication_status: published
status: public
title: Switching time optimization in discretized hybrid dynamical systems
type: conference
user_id: '15701'
year: '2012'
...
---
_id: '24170'
article_number: '045016'
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Patrick
full_name: Gelß, Patrick
last_name: Gelß
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Frank
full_name: Noé, Frank
last_name: Noé
citation:
ama: 'Klus S, Gelß P, Nüske F, Noé F. Symmetric and antisymmetric kernels for machine
learning problems in quantum physics and chemistry. Machine Learning: Science
and Technology. Published online 2021. doi:10.1088/2632-2153/ac14ad'
apa: 'Klus, S., Gelß, P., Nüske, F., & Noé, F. (2021). Symmetric and antisymmetric
kernels for machine learning problems in quantum physics and chemistry. Machine
Learning: Science and Technology, Article 045016. https://doi.org/10.1088/2632-2153/ac14ad'
bibtex: '@article{Klus_Gelß_Nüske_Noé_2021, title={Symmetric and antisymmetric kernels
for machine learning problems in quantum physics and chemistry}, DOI={10.1088/2632-2153/ac14ad},
number={045016}, journal={Machine Learning: Science and Technology}, author={Klus,
Stefan and Gelß, Patrick and Nüske, Feliks and Noé, Frank}, year={2021} }'
chicago: 'Klus, Stefan, Patrick Gelß, Feliks Nüske, and Frank Noé. “Symmetric and
Antisymmetric Kernels for Machine Learning Problems in Quantum Physics and Chemistry.”
Machine Learning: Science and Technology, 2021. https://doi.org/10.1088/2632-2153/ac14ad.'
ieee: 'S. Klus, P. Gelß, F. Nüske, and F. Noé, “Symmetric and antisymmetric kernels
for machine learning problems in quantum physics and chemistry,” Machine Learning:
Science and Technology, Art. no. 045016, 2021, doi: 10.1088/2632-2153/ac14ad.'
mla: 'Klus, Stefan, et al. “Symmetric and Antisymmetric Kernels for Machine Learning
Problems in Quantum Physics and Chemistry.” Machine Learning: Science and Technology,
045016, 2021, doi:10.1088/2632-2153/ac14ad.'
short: 'S. Klus, P. Gelß, F. Nüske, F. Noé, Machine Learning: Science and Technology
(2021).'
date_created: 2021-09-12T08:52:57Z
date_updated: 2022-01-06T06:56:08Z
department:
- _id: '101'
doi: 10.1088/2632-2153/ac14ad
language:
- iso: eng
publication: 'Machine Learning: Science and Technology'
publication_identifier:
issn:
- 2632-2153
publication_status: published
status: public
title: Symmetric and antisymmetric kernels for machine learning problems in quantum
physics and chemistry
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '16636'
author:
- first_name: A.
full_name: Meyer, A.
last_name: Meyer
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
citation:
ama: Meyer A, Dellnitz M. Symmetries in Timed Continuous Petri Nets. IFAC Proceedings
Volumes. 2009:68-73. doi:10.3182/20090916-3-es-3003.00013
apa: Meyer, A., & Dellnitz, M. (2009). Symmetries in Timed Continuous Petri
Nets. IFAC Proceedings Volumes, 68–73. https://doi.org/10.3182/20090916-3-es-3003.00013
bibtex: '@article{Meyer_Dellnitz_2009, title={Symmetries in Timed Continuous Petri
Nets}, DOI={10.3182/20090916-3-es-3003.00013},
journal={IFAC Proceedings Volumes}, author={Meyer, A. and Dellnitz, M.}, year={2009},
pages={68–73} }'
chicago: Meyer, A., and M. Dellnitz. “Symmetries in Timed Continuous Petri Nets.”
IFAC Proceedings Volumes, 2009, 68–73. https://doi.org/10.3182/20090916-3-es-3003.00013.
ieee: A. Meyer and M. Dellnitz, “Symmetries in Timed Continuous Petri Nets,” IFAC
Proceedings Volumes, pp. 68–73, 2009.
mla: Meyer, A., and M. Dellnitz. “Symmetries in Timed Continuous Petri Nets.” IFAC
Proceedings Volumes, 2009, pp. 68–73, doi:10.3182/20090916-3-es-3003.00013.
short: A. Meyer, M. Dellnitz, IFAC Proceedings Volumes (2009) 68–73.
date_created: 2020-04-16T08:34:44Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.3182/20090916-3-es-3003.00013
language:
- iso: eng
page: 68-73
publication: IFAC Proceedings Volumes
publication_identifier:
issn:
- 1474-6670
publication_status: published
status: public
title: Symmetries in Timed Continuous Petri Nets
type: journal_article
user_id: '15701'
year: '2009'
...
---
_id: '16639'
author:
- first_name: A.
full_name: Meyer, A.
last_name: Meyer
- first_name: M.
full_name: Dellnitz, M.
last_name: Dellnitz
- first_name: M.
full_name: Hessel-von Molo, M.
last_name: Hessel-von Molo
citation:
ama: 'Meyer A, Dellnitz M, Hessel-von Molo M. Symmetries in timed continuous Petri
nets. Nonlinear Analysis: Hybrid Systems. 2011:125-135. doi:10.1016/j.nahs.2010.05.005'
apa: 'Meyer, A., Dellnitz, M., & Hessel-von Molo, M. (2011). Symmetries in timed
continuous Petri nets. Nonlinear Analysis: Hybrid Systems, 125–135. https://doi.org/10.1016/j.nahs.2010.05.005'
bibtex: '@article{Meyer_Dellnitz_Hessel-von Molo_2011, title={Symmetries in timed
continuous Petri nets}, DOI={10.1016/j.nahs.2010.05.005},
journal={Nonlinear Analysis: Hybrid Systems}, author={Meyer, A. and Dellnitz,
M. and Hessel-von Molo, M.}, year={2011}, pages={125–135} }'
chicago: 'Meyer, A., M. Dellnitz, and M. Hessel-von Molo. “Symmetries in Timed Continuous
Petri Nets.” Nonlinear Analysis: Hybrid Systems, 2011, 125–35. https://doi.org/10.1016/j.nahs.2010.05.005.'
ieee: 'A. Meyer, M. Dellnitz, and M. Hessel-von Molo, “Symmetries in timed continuous
Petri nets,” Nonlinear Analysis: Hybrid Systems, pp. 125–135, 2011.'
mla: 'Meyer, A., et al. “Symmetries in Timed Continuous Petri Nets.” Nonlinear
Analysis: Hybrid Systems, 2011, pp. 125–35, doi:10.1016/j.nahs.2010.05.005.'
short: 'A. Meyer, M. Dellnitz, M. Hessel-von Molo, Nonlinear Analysis: Hybrid Systems
(2011) 125–135.'
date_created: 2020-04-16T08:57:00Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1016/j.nahs.2010.05.005
language:
- iso: eng
page: 125-135
publication: 'Nonlinear Analysis: Hybrid Systems'
publication_identifier:
issn:
- 1751-570X
publication_status: published
status: public
title: Symmetries in timed continuous Petri nets
type: journal_article
user_id: '15701'
year: '2011'
...
---
_id: '16510'
abstract:
- lang: eng
text: In an array of coupled oscillators, synchronous chaos may occur in
the sense that all the oscillators behave identically although the corresponding
motion is chaotic. When a parameter is varied this fully symmetric dynamical state
can lose its stability, and the main purpose of this paper is to investigate which
type of dynamical behavior is expected to be observed once the loss of stability
has occurred. The essential tool is a classification of Lyapunov exponents based
on the symmetry of the underlying problem. This classification is crucial in the
derivation of the analytical results but it also allows an efficient computation
of the dominant Lyapunov exponent associated with each symmetry type. We show
how these dominant exponents determine the stability of invariant sets possessing
various instantaneous symmetries, and this leads to the idea of symmetry breaking
bifurcations of chaotic attractors. Finally, the results and ideas are illustrated
for several systems of coupled oscillators.
author:
- first_name: Philip J.
full_name: Aston, Philip J.
last_name: Aston
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Aston PJ, Dellnitz M. Symmetry Breaking Bifurcations of Chaotic Attractors.
International Journal of Bifurcation and Chaos. 1995:1643-1676. doi:10.1142/s021812749500123x
apa: Aston, P. J., & Dellnitz, M. (1995). Symmetry Breaking Bifurcations of
Chaotic Attractors. International Journal of Bifurcation and Chaos, 1643–1676.
https://doi.org/10.1142/s021812749500123x
bibtex: '@article{Aston_Dellnitz_1995, title={Symmetry Breaking Bifurcations of
Chaotic Attractors}, DOI={10.1142/s021812749500123x},
journal={International Journal of Bifurcation and Chaos}, author={Aston, Philip
J. and Dellnitz, Michael}, year={1995}, pages={1643–1676} }'
chicago: Aston, Philip J., and Michael Dellnitz. “Symmetry Breaking Bifurcations
of Chaotic Attractors.” International Journal of Bifurcation and Chaos,
1995, 1643–76. https://doi.org/10.1142/s021812749500123x.
ieee: P. J. Aston and M. Dellnitz, “Symmetry Breaking Bifurcations of Chaotic Attractors,”
International Journal of Bifurcation and Chaos, pp. 1643–1676, 1995.
mla: Aston, Philip J., and Michael Dellnitz. “Symmetry Breaking Bifurcations of
Chaotic Attractors.” International Journal of Bifurcation and Chaos, 1995,
pp. 1643–76, doi:10.1142/s021812749500123x.
short: P.J. Aston, M. Dellnitz, International Journal of Bifurcation and Chaos (1995)
1643–1676.
date_created: 2020-04-15T07:23:50Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1142/s021812749500123x
language:
- iso: eng
page: 1643-1676
publication: International Journal of Bifurcation and Chaos
publication_identifier:
issn:
- 0218-1274
- 1793-6551
publication_status: published
status: public
title: Symmetry Breaking Bifurcations of Chaotic Attractors
type: journal_article
user_id: '15701'
year: '1995'
...
---
_id: '17039'
author:
- first_name: Kathrin
full_name: Flasskamp, Kathrin
last_name: Flasskamp
- first_name: Sebastian
full_name: Hage-Packhäuser, Sebastian
last_name: Hage-Packhäuser
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
citation:
ama: Flasskamp K, Hage-Packhäuser S, Ober-Blöbaum S. Symmetry exploiting control
of hybrid mechanical systems. Journal of Computational Dynamics. 2015;2(1):25-50.
doi:10.3934/jcd.2015.2.25
apa: Flasskamp, K., Hage-Packhäuser, S., & Ober-Blöbaum, S. (2015). Symmetry
exploiting control of hybrid mechanical systems. Journal of Computational Dynamics,
2(1), 25–50. https://doi.org/10.3934/jcd.2015.2.25
bibtex: '@article{Flasskamp_Hage-Packhäuser_Ober-Blöbaum_2015, title={Symmetry exploiting
control of hybrid mechanical systems}, volume={2}, DOI={10.3934/jcd.2015.2.25},
number={1}, journal={Journal of Computational Dynamics}, author={Flasskamp, Kathrin
and Hage-Packhäuser, Sebastian and Ober-Blöbaum, Sina}, year={2015}, pages={25–50}
}'
chicago: 'Flasskamp, Kathrin, Sebastian Hage-Packhäuser, and Sina Ober-Blöbaum.
“Symmetry Exploiting Control of Hybrid Mechanical Systems.” Journal of Computational
Dynamics 2, no. 1 (2015): 25–50. https://doi.org/10.3934/jcd.2015.2.25.'
ieee: K. Flasskamp, S. Hage-Packhäuser, and S. Ober-Blöbaum, “Symmetry exploiting
control of hybrid mechanical systems,” Journal of Computational Dynamics,
vol. 2, no. 1, pp. 25–50, 2015.
mla: Flasskamp, Kathrin, et al. “Symmetry Exploiting Control of Hybrid Mechanical
Systems.” Journal of Computational Dynamics, vol. 2, no. 1, 2015, pp. 25–50,
doi:10.3934/jcd.2015.2.25.
short: K. Flasskamp, S. Hage-Packhäuser, S. Ober-Blöbaum, Journal of Computational
Dynamics 2 (2015) 25–50.
date_created: 2020-05-20T08:18:06Z
date_updated: 2022-01-06T06:53:03Z
department:
- _id: '101'
doi: 10.3934/jcd.2015.2.25
intvolume: ' 2'
issue: '1'
language:
- iso: eng
page: 25-50
publication: Journal of Computational Dynamics
status: public
title: Symmetry exploiting control of hybrid mechanical systems
type: journal_article
user_id: '47427'
volume: 2
year: '2015'
...
---
_id: '17411'
abstract:
- lang: eng
text: Many dynamical systems possess symmetries, e.g. rotational and translational
invariances of mechanical systems. These can be beneficially exploited in the
design of numerical optimal control methods. We present a model predictive control
scheme which is based on a library of precomputed motion primitives. The primitives
are equivalence classes w.r.t. the symmetry of the optimal control problems. Trim
primitives as relative equilibria w.r.t. this symmetry, play a crucial role in
the algorithm. The approach is illustrated using an academic mobile robot example.
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: 0000-0002-3389-793X
citation:
ama: 'Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in Optimal Control: A Multiobjective
Model Predictive Control Approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum
S, Padberg-Gehle K, eds. Advances in Dynamics, Optimization and Computation.
Cham: Springer; 2020. doi:10.1007/978-3-030-51264-4_9'
apa: 'Flaßkamp, K., Ober-Blöbaum, S., & Peitz, S. (2020). Symmetry in Optimal
Control: A Multiobjective Model Predictive Control Approach. In O. Junge, O. Schütze,
G. Froyland, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics,
Optimization and Computation. Cham: Springer. https://doi.org/10.1007/978-3-030-51264-4_9'
bibtex: '@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry
in Optimal Control: A Multiobjective Model Predictive Control Approach}, DOI={10.1007/978-3-030-51264-4_9},
booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer},
author={Flaßkamp, Kathrin and Ober-Blöbaum, Sina and Peitz, Sebastian}, editor={Junge,
Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle,
KathrinEditors}, year={2020} }'
chicago: 'Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Sebastian Peitz. “Symmetry in
Optimal Control: A Multiobjective Model Predictive Control Approach.” In Advances
in Dynamics, Optimization and Computation, edited by Oliver Junge, Oliver
Schütze, Gary Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle. Cham: Springer,
2020. https://doi.org/10.1007/978-3-030-51264-4_9.'
ieee: 'K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in Optimal Control:
A Multiobjective Model Predictive Control Approach,” in Advances in Dynamics,
Optimization and Computation, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum,
and K. Padberg-Gehle, Eds. Cham: Springer, 2020.'
mla: 'Flaßkamp, Kathrin, et al. “Symmetry in Optimal Control: A Multiobjective Model
Predictive Control Approach.” Advances in Dynamics, Optimization and Computation,
edited by Oliver Junge et al., Springer, 2020, doi:10.1007/978-3-030-51264-4_9.'
short: 'K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland,
S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and
Computation, Springer, Cham, 2020.'
date_created: 2020-07-27T09:50:19Z
date_updated: 2022-01-06T06:53:11Z
department:
- _id: '101'
doi: 10.1007/978-3-030-51264-4_9
editor:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Padberg-Gehle, Kathrin
last_name: Padberg-Gehle
language:
- iso: eng
place: Cham
publication: Advances in Dynamics, Optimization and Computation
publication_identifier:
isbn:
- '9783030512637'
- '9783030512644'
issn:
- 2198-4182
- 2198-4190
publication_status: published
publisher: Springer
status: public
title: 'Symmetry in Optimal Control: A Multiobjective Model Predictive Control Approach'
type: book_chapter
user_id: '47427'
year: '2020'
...
---
_id: '16549'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Martin
full_name: Golubitsky, Martin
last_name: Golubitsky
- first_name: Matthew
full_name: Nicol, Matthew
last_name: Nicol
citation:
ama: 'Dellnitz M, Golubitsky M, Nicol M. Symmetry of Attractors and the Karhunen-Loève
Decomposition. In: Trends and Perspectives in Applied Mathematics. New
York, NY; 1994. doi:10.1007/978-1-4612-0859-4_4'
apa: Dellnitz, M., Golubitsky, M., & Nicol, M. (1994). Symmetry of Attractors
and the Karhunen-Loève Decomposition. In Trends and Perspectives in Applied
Mathematics. New York, NY. https://doi.org/10.1007/978-1-4612-0859-4_4
bibtex: '@inbook{Dellnitz_Golubitsky_Nicol_1994, place={New York, NY}, title={Symmetry
of Attractors and the Karhunen-Loève Decomposition}, DOI={10.1007/978-1-4612-0859-4_4},
booktitle={Trends and Perspectives in Applied Mathematics}, author={Dellnitz,
Michael and Golubitsky, Martin and Nicol, Matthew}, year={1994} }'
chicago: Dellnitz, Michael, Martin Golubitsky, and Matthew Nicol. “Symmetry of Attractors
and the Karhunen-Loève Decomposition.” In Trends and Perspectives in Applied
Mathematics. New York, NY, 1994. https://doi.org/10.1007/978-1-4612-0859-4_4.
ieee: M. Dellnitz, M. Golubitsky, and M. Nicol, “Symmetry of Attractors and the
Karhunen-Loève Decomposition,” in Trends and Perspectives in Applied Mathematics,
New York, NY, 1994.
mla: Dellnitz, Michael, et al. “Symmetry of Attractors and the Karhunen-Loève Decomposition.”
Trends and Perspectives in Applied Mathematics, 1994, doi:10.1007/978-1-4612-0859-4_4.
short: 'M. Dellnitz, M. Golubitsky, M. Nicol, in: Trends and Perspectives in Applied
Mathematics, New York, NY, 1994.'
date_created: 2020-04-15T09:02:32Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-1-4612-0859-4_4
language:
- iso: eng
place: New York, NY
publication: Trends and Perspectives in Applied Mathematics
publication_identifier:
isbn:
- '9781461269243'
- '9781461208594'
issn:
- 0066-5452
publication_status: published
status: public
title: Symmetry of Attractors and the Karhunen-Loève Decomposition
type: book_chapter
user_id: '15701'
year: '1994'
...
---
_id: '16632'
author:
- first_name: Prashant G.
full_name: Mehta, Prashant G.
last_name: Mehta
- first_name: Mirko
full_name: Hessel-von Molo, Mirko
last_name: Hessel-von Molo
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Mehta PG, Hessel-von Molo M, Dellnitz M. Symmetry of attractors and the Perron-Frobenius
operator. Journal of Difference Equations and Applications. 2006:1147-1178.
doi:10.1080/10236190601045788
apa: Mehta, P. G., Hessel-von Molo, M., & Dellnitz, M. (2006). Symmetry of attractors
and the Perron-Frobenius operator. Journal of Difference Equations and Applications,
1147–1178. https://doi.org/10.1080/10236190601045788
bibtex: '@article{Mehta_Hessel-von Molo_Dellnitz_2006, title={Symmetry of attractors
and the Perron-Frobenius operator}, DOI={10.1080/10236190601045788},
journal={Journal of Difference Equations and Applications}, author={Mehta, Prashant
G. and Hessel-von Molo, Mirko and Dellnitz, Michael}, year={2006}, pages={1147–1178}
}'
chicago: Mehta, Prashant G., Mirko Hessel-von Molo, and Michael Dellnitz. “Symmetry
of Attractors and the Perron-Frobenius Operator.” Journal of Difference Equations
and Applications, 2006, 1147–78. https://doi.org/10.1080/10236190601045788.
ieee: P. G. Mehta, M. Hessel-von Molo, and M. Dellnitz, “Symmetry of attractors
and the Perron-Frobenius operator,” Journal of Difference Equations and Applications,
pp. 1147–1178, 2006.
mla: Mehta, Prashant G., et al. “Symmetry of Attractors and the Perron-Frobenius
Operator.” Journal of Difference Equations and Applications, 2006, pp.
1147–78, doi:10.1080/10236190601045788.
short: P.G. Mehta, M. Hessel-von Molo, M. Dellnitz, Journal of Difference Equations
and Applications (2006) 1147–1178.
date_created: 2020-04-16T08:30:46Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.1080/10236190601045788
language:
- iso: eng
page: 1147-1178
publication: Journal of Difference Equations and Applications
publication_identifier:
issn:
- 1023-6198
- 1563-5120
publication_status: published
status: public
title: Symmetry of attractors and the Perron-Frobenius operator
type: journal_article
user_id: '15701'
year: '2006'
...
---
_id: '16638'
author:
- first_name: A.
full_name: Meyer, A.
last_name: Meyer
- first_name: M.
full_name: Silva, M.
last_name: Silva
citation:
ama: Meyer A, Silva M. Symmetry Reductions in Timed Continuous Petri Nets Under
Infinite Server Semantics. IFAC Proceedings Volumes. 2012:153-159. doi:10.3182/20120606-3-nl-3011.00067
apa: Meyer, A., & Silva, M. (2012). Symmetry Reductions in Timed Continuous
Petri Nets Under Infinite Server Semantics. IFAC Proceedings Volumes, 153–159.
https://doi.org/10.3182/20120606-3-nl-3011.00067
bibtex: '@article{Meyer_Silva_2012, title={Symmetry Reductions in Timed Continuous
Petri Nets Under Infinite Server Semantics}, DOI={10.3182/20120606-3-nl-3011.00067},
journal={IFAC Proceedings Volumes}, author={Meyer, A. and Silva, M.}, year={2012},
pages={153–159} }'
chicago: Meyer, A., and M. Silva. “Symmetry Reductions in Timed Continuous Petri
Nets Under Infinite Server Semantics.” IFAC Proceedings Volumes, 2012,
153–59. https://doi.org/10.3182/20120606-3-nl-3011.00067.
ieee: A. Meyer and M. Silva, “Symmetry Reductions in Timed Continuous Petri Nets
Under Infinite Server Semantics,” IFAC Proceedings Volumes, pp. 153–159,
2012.
mla: Meyer, A., and M. Silva. “Symmetry Reductions in Timed Continuous Petri Nets
Under Infinite Server Semantics.” IFAC Proceedings Volumes, 2012, pp. 153–59,
doi:10.3182/20120606-3-nl-3011.00067.
short: A. Meyer, M. Silva, IFAC Proceedings Volumes (2012) 153–159.
date_created: 2020-04-16T08:52:25Z
date_updated: 2022-01-06T06:52:53Z
department:
- _id: '101'
doi: 10.3182/20120606-3-nl-3011.00067
language:
- iso: eng
page: 153-159
publication: IFAC Proceedings Volumes
publication_identifier:
issn:
- 1474-6670
publication_status: published
status: public
title: Symmetry Reductions in Timed Continuous Petri Nets Under Infinite Server Semantics
type: journal_article
user_id: '15701'
year: '2012'
...
---
_id: '24169'
article_number: '133018'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Patrick
full_name: Gelß, Patrick
last_name: Gelß
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Cecilia
full_name: Clementi, Cecilia
last_name: Clementi
citation:
ama: 'Nüske F, Gelß P, Klus S, Clementi C. Tensor-based computation of metastable
and coherent sets. Physica D: Nonlinear Phenomena. Published online 2021.
doi:10.1016/j.physd.2021.133018'
apa: 'Nüske, F., Gelß, P., Klus, S., & Clementi, C. (2021). Tensor-based computation
of metastable and coherent sets. Physica D: Nonlinear Phenomena, Article
133018. https://doi.org/10.1016/j.physd.2021.133018'
bibtex: '@article{Nüske_Gelß_Klus_Clementi_2021, title={Tensor-based computation
of metastable and coherent sets}, DOI={10.1016/j.physd.2021.133018},
number={133018}, journal={Physica D: Nonlinear Phenomena}, author={Nüske, Feliks
and Gelß, Patrick and Klus, Stefan and Clementi, Cecilia}, year={2021} }'
chicago: 'Nüske, Feliks, Patrick Gelß, Stefan Klus, and Cecilia Clementi. “Tensor-Based
Computation of Metastable and Coherent Sets.” Physica D: Nonlinear Phenomena,
2021. https://doi.org/10.1016/j.physd.2021.133018.'
ieee: 'F. Nüske, P. Gelß, S. Klus, and C. Clementi, “Tensor-based computation of
metastable and coherent sets,” Physica D: Nonlinear Phenomena, Art. no.
133018, 2021, doi: 10.1016/j.physd.2021.133018.'
mla: 'Nüske, Feliks, et al. “Tensor-Based Computation of Metastable and Coherent
Sets.” Physica D: Nonlinear Phenomena, 133018, 2021, doi:10.1016/j.physd.2021.133018.'
short: 'F. Nüske, P. Gelß, S. Klus, C. Clementi, Physica D: Nonlinear Phenomena
(2021).'
date_created: 2021-09-12T08:51:24Z
date_updated: 2022-01-06T06:56:08Z
department:
- _id: '101'
doi: 10.1016/j.physd.2021.133018
language:
- iso: eng
publication: 'Physica D: Nonlinear Phenomena'
publication_identifier:
issn:
- 0167-2789
publication_status: published
status: public
title: Tensor-based computation of metastable and coherent sets
type: journal_article
user_id: '81513'
year: '2021'
...
---
_id: '8755'
abstract:
- lang: eng
text: Dynamic mode decomposition (DMD) is a recently developed tool for the analysis
of the behavior of complex dynamical systems. In this paper, we will propose an
extension of DMD that exploits low-rank tensor decompositions of potentially high-dimensional
data sets to compute the corresponding DMD modes and eigenvalues. The goal is
to reduce the computational complexity and also the amount of memory required
to store the data in order to mitigate the curse of dimensionality. The efficiency
of these tensor-based methods will be illustrated with the aid of several different
fluid dynamics problems such as the von Kármán vortex street and the simulation
of two merging vortices.
article_type: original
author:
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Patrick
full_name: Gelß, Patrick
last_name: Gelß
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Christof
full_name: Schütte, Christof
last_name: Schütte
citation:
ama: Klus S, Gelß P, Peitz S, Schütte C. Tensor-based dynamic mode decomposition.
Nonlinearity. 2018;31(7):3359-3380. doi:10.1088/1361-6544/aabc8f
apa: Klus, S., Gelß, P., Peitz, S., & Schütte, C. (2018). Tensor-based dynamic
mode decomposition. Nonlinearity, 31(7), 3359–3380. https://doi.org/10.1088/1361-6544/aabc8f
bibtex: '@article{Klus_Gelß_Peitz_Schütte_2018, title={Tensor-based dynamic mode
decomposition}, volume={31}, DOI={10.1088/1361-6544/aabc8f},
number={7}, journal={Nonlinearity}, author={Klus, Stefan and Gelß, Patrick and
Peitz, Sebastian and Schütte, Christof}, year={2018}, pages={3359–3380} }'
chicago: 'Klus, Stefan, Patrick Gelß, Sebastian Peitz, and Christof Schütte. “Tensor-Based
Dynamic Mode Decomposition.” Nonlinearity 31, no. 7 (2018): 3359–80. https://doi.org/10.1088/1361-6544/aabc8f.'
ieee: S. Klus, P. Gelß, S. Peitz, and C. Schütte, “Tensor-based dynamic mode decomposition,”
Nonlinearity, vol. 31, no. 7, pp. 3359–3380, 2018.
mla: Klus, Stefan, et al. “Tensor-Based Dynamic Mode Decomposition.” Nonlinearity,
vol. 31, no. 7, 2018, pp. 3359–80, doi:10.1088/1361-6544/aabc8f.
short: S. Klus, P. Gelß, S. Peitz, C. Schütte, Nonlinearity 31 (2018) 3359–3380.
date_created: 2019-03-29T13:32:04Z
date_updated: 2022-01-06T07:04:00Z
department:
- _id: '101'
doi: 10.1088/1361-6544/aabc8f
intvolume: ' 31'
issue: '7'
language:
- iso: eng
page: 3359-3380
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
status: public
title: Tensor-based dynamic mode decomposition
type: journal_article
user_id: '47427'
volume: 31
year: '2018'
...
---
_id: '16555'
author:
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
citation:
ama: 'Dellnitz M, Froyland G, Junge O. The Algorithms Behind GAIO — Set Oriented
Numerical Methods for Dynamical Systems. In: Ergodic Theory, Analysis, and
Efficient Simulation of Dynamical Systems. Berlin, Heidelberg; 2001. doi:10.1007/978-3-642-56589-2_7'
apa: Dellnitz, M., Froyland, G., & Junge, O. (2001). The Algorithms Behind GAIO
— Set Oriented Numerical Methods for Dynamical Systems. In Ergodic Theory,
Analysis, and Efficient Simulation of Dynamical Systems. Berlin, Heidelberg.
https://doi.org/10.1007/978-3-642-56589-2_7
bibtex: '@inbook{Dellnitz_Froyland_Junge_2001, place={Berlin, Heidelberg}, title={The
Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems},
DOI={10.1007/978-3-642-56589-2_7},
booktitle={Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems},
author={Dellnitz, Michael and Froyland, Gary and Junge, Oliver}, year={2001} }'
chicago: Dellnitz, Michael, Gary Froyland, and Oliver Junge. “The Algorithms Behind
GAIO — Set Oriented Numerical Methods for Dynamical Systems.” In Ergodic Theory,
Analysis, and Efficient Simulation of Dynamical Systems. Berlin, Heidelberg,
2001. https://doi.org/10.1007/978-3-642-56589-2_7.
ieee: M. Dellnitz, G. Froyland, and O. Junge, “The Algorithms Behind GAIO — Set
Oriented Numerical Methods for Dynamical Systems,” in Ergodic Theory, Analysis,
and Efficient Simulation of Dynamical Systems, Berlin, Heidelberg, 2001.
mla: Dellnitz, Michael, et al. “The Algorithms Behind GAIO — Set Oriented Numerical
Methods for Dynamical Systems.” Ergodic Theory, Analysis, and Efficient Simulation
of Dynamical Systems, 2001, doi:10.1007/978-3-642-56589-2_7.
short: 'M. Dellnitz, G. Froyland, O. Junge, in: Ergodic Theory, Analysis, and Efficient
Simulation of Dynamical Systems, Berlin, Heidelberg, 2001.'
date_created: 2020-04-15T09:10:54Z
date_updated: 2022-01-06T06:52:52Z
department:
- _id: '101'
doi: 10.1007/978-3-642-56589-2_7
language:
- iso: eng
place: Berlin, Heidelberg
publication: Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems
publication_identifier:
isbn:
- '9783642625244'
- '9783642565892'
publication_status: published
status: public
title: The Algorithms Behind GAIO — Set Oriented Numerical Methods for Dynamical Systems
type: book_chapter
user_id: '15701'
year: '2001'
...
---
_id: '17994'
abstract:
- lang: eng
text: In this work we review the novel framework for the computation of finite dimensional
invariant sets of infinite dimensional dynamical systems developed in [6] and
[36]. By utilizing results on embedding techniques for infinite dimensional systems
we extend a classical subdivision scheme [8] as well as a continuation algorithm
[7] for the computation of attractors and invariant manifolds of finite dimensional
systems to the infinite dimensional case. We show how to implement this approach
for the analysis of delay differential equations and partial differential equations
and illustrate the feasibility of our implementation by computing the attractor
of the Mackey-Glass equation and the unstable manifold of the one-dimensional
Kuramoto-Sivashinsky equation.
author:
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
- first_name: Adrian
full_name: Ziessler, Adrian
last_name: Ziessler
citation:
ama: 'Gerlach R, Ziessler A. The Approximation of Invariant Sets in Infinite Dimensional
Dynamical Systems. In: Junge O, Schütze O, Ober-Blöbaum S, Padberg-Gehle K, eds.
Advances in Dynamics, Optimization and Computation. Vol 304. Studies in
Systems, Decision and Control. Springer International Publishing; 2020:66-85.
doi:10.1007/978-3-030-51264-4_3'
apa: Gerlach, R., & Ziessler, A. (2020). The Approximation of Invariant Sets
in Infinite Dimensional Dynamical Systems. In O. Junge, O. Schütze, S. Ober-Blöbaum,
& K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and Computation
(Vol. 304, pp. 66–85). Springer International Publishing. https://doi.org/10.1007/978-3-030-51264-4_3
bibtex: '@inbook{Gerlach_Ziessler_2020, place={Cham}, series={Studies in Systems,
Decision and Control}, title={The Approximation of Invariant Sets in Infinite
Dimensional Dynamical Systems}, volume={304}, DOI={10.1007/978-3-030-51264-4_3},
booktitle={Advances in Dynamics, Optimization and Computation}, publisher={Springer
International Publishing}, author={Gerlach, Raphael and Ziessler, Adrian}, editor={Junge,
Oliver and Schütze, Oliver and Ober-Blöbaum, Sina and Padberg-Gehle, Kathrin},
year={2020}, pages={66–85}, collection={Studies in Systems, Decision and Control}
}'
chicago: 'Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant
Sets in Infinite Dimensional Dynamical Systems.” In Advances in Dynamics, Optimization
and Computation, edited by Oliver Junge, Oliver Schütze, Sina Ober-Blöbaum,
and Kathrin Padberg-Gehle, 304:66–85. Studies in Systems, Decision and Control.
Cham: Springer International Publishing, 2020. https://doi.org/10.1007/978-3-030-51264-4_3.'
ieee: 'R. Gerlach and A. Ziessler, “The Approximation of Invariant Sets in Infinite
Dimensional Dynamical Systems,” in Advances in Dynamics, Optimization and Computation,
vol. 304, O. Junge, O. Schütze, S. Ober-Blöbaum, and K. Padberg-Gehle, Eds. Cham:
Springer International Publishing, 2020, pp. 66–85.'
mla: Gerlach, Raphael, and Adrian Ziessler. “The Approximation of Invariant Sets
in Infinite Dimensional Dynamical Systems.” Advances in Dynamics, Optimization
and Computation, edited by Oliver Junge et al., vol. 304, Springer International
Publishing, 2020, pp. 66–85, doi:10.1007/978-3-030-51264-4_3.
short: 'R. Gerlach, A. Ziessler, in: O. Junge, O. Schütze, S. Ober-Blöbaum, K. Padberg-Gehle
(Eds.), Advances in Dynamics, Optimization and Computation, Springer International
Publishing, Cham, 2020, pp. 66–85.'
date_created: 2020-08-14T15:02:22Z
date_updated: 2023-11-17T13:13:25Z
department:
- _id: '101'
doi: 10.1007/978-3-030-51264-4_3
editor:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Padberg-Gehle, Kathrin
last_name: Padberg-Gehle
intvolume: ' 304'
language:
- iso: eng
main_file_link:
- url: https://link.springer.com/chapter/10.1007/978-3-030-51264-4_3
page: 66-85
place: Cham
publication: Advances in Dynamics, Optimization and Computation
publication_identifier:
isbn:
- '9783030512637'
- '9783030512644'
issn:
- 2198-4182
- 2198-4190
publication_status: published
publisher: Springer International Publishing
series_title: Studies in Systems, Decision and Control
status: public
title: The Approximation of Invariant Sets in Infinite Dimensional Dynamical Systems
type: book_chapter
user_id: '32655'
volume: 304
year: '2020'
...