---
_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: '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: '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: '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: '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: '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: '16715'
author:
- first_name: Andreas
full_name: Bittracher, Andreas
last_name: Bittracher
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Ralf
full_name: Banisch, Ralf
last_name: Banisch
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Christof
full_name: Schütte, Christof
last_name: Schütte
citation:
ama: Bittracher A, Koltai P, Klus S, Banisch R, Dellnitz M, Schütte C. Transition
Manifolds of Complex Metastable Systems. Journal of Nonlinear Science.
2018;28:471-512. doi:10.1007/s00332-017-9415-0
apa: Bittracher, A., Koltai, P., Klus, S., Banisch, R., Dellnitz, M., & Schütte,
C. (2018). Transition Manifolds of Complex Metastable Systems. Journal of Nonlinear
Science, 28, 471–512. https://doi.org/10.1007/s00332-017-9415-0
bibtex: '@article{Bittracher_Koltai_Klus_Banisch_Dellnitz_Schütte_2018, title={Transition
Manifolds of Complex Metastable Systems}, volume={28}, DOI={10.1007/s00332-017-9415-0},
journal={Journal of Nonlinear Science}, author={Bittracher, Andreas and Koltai,
Péter and Klus, Stefan and Banisch, Ralf and Dellnitz, Michael and Schütte, Christof},
year={2018}, pages={471–512} }'
chicago: 'Bittracher, Andreas, Péter Koltai, Stefan Klus, Ralf Banisch, Michael
Dellnitz, and Christof Schütte. “Transition Manifolds of Complex Metastable Systems.”
Journal of Nonlinear Science 28 (2018): 471–512. https://doi.org/10.1007/s00332-017-9415-0.'
ieee: A. Bittracher, P. Koltai, S. Klus, R. Banisch, M. Dellnitz, and C. Schütte,
“Transition Manifolds of Complex Metastable Systems,” Journal of Nonlinear
Science, vol. 28, pp. 471–512, 2018.
mla: Bittracher, Andreas, et al. “Transition Manifolds of Complex Metastable Systems.”
Journal of Nonlinear Science, vol. 28, 2018, pp. 471–512, doi:10.1007/s00332-017-9415-0.
short: A. Bittracher, P. Koltai, S. Klus, R. Banisch, M. Dellnitz, C. Schütte, Journal
of Nonlinear Science 28 (2018) 471–512.
date_created: 2020-04-16T14:09:31Z
date_updated: 2022-01-06T06:52:55Z
department:
- _id: '101'
doi: 10.1007/s00332-017-9415-0
intvolume: ' 28'
language:
- iso: eng
page: 471-512
publication: Journal of Nonlinear Science
publication_identifier:
issn:
- 0938-8974
- 1432-1467
publication_status: published
status: public
title: Transition Manifolds of Complex Metastable Systems
type: journal_article
user_id: '47427'
volume: 28
year: '2018'
...
---
_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: '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: '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: '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: '21939'
article_number: '154104'
author:
- 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: Fabian
full_name: Paul, Fabian
last_name: Paul
- first_name: Stefan
full_name: Klus, Stefan
last_name: Klus
- first_name: Péter
full_name: Koltai, Péter
last_name: Koltai
- first_name: Frank
full_name: Noé, Frank
last_name: Noé
citation:
ama: 'Wu H, Nüske F, Paul F, Klus S, Koltai P, Noé F. Variational Koopman models:
Slow collective variables and molecular kinetics from short off-equilibrium simulations.
The Journal of Chemical Physics. 2017. doi:10.1063/1.4979344'
apa: 'Wu, H., Nüske, F., Paul, F., Klus, S., Koltai, P., & Noé, F. (2017). Variational
Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium
simulations. The Journal of Chemical Physics. https://doi.org/10.1063/1.4979344'
bibtex: '@article{Wu_Nüske_Paul_Klus_Koltai_Noé_2017, title={Variational Koopman
models: Slow collective variables and molecular kinetics from short off-equilibrium
simulations}, DOI={10.1063/1.4979344},
number={154104}, journal={The Journal of Chemical Physics}, author={Wu, Hao and
Nüske, Feliks and Paul, Fabian and Klus, Stefan and Koltai, Péter and Noé, Frank},
year={2017} }'
chicago: 'Wu, Hao, Feliks Nüske, Fabian Paul, Stefan Klus, Péter Koltai, and Frank
Noé. “Variational Koopman Models: Slow Collective Variables and Molecular Kinetics
from Short off-Equilibrium Simulations.” The Journal of Chemical Physics,
2017. https://doi.org/10.1063/1.4979344.'
ieee: 'H. Wu, F. Nüske, F. Paul, S. Klus, P. Koltai, and F. Noé, “Variational Koopman
models: Slow collective variables and molecular kinetics from short off-equilibrium
simulations,” The Journal of Chemical Physics, 2017.'
mla: 'Wu, Hao, et al. “Variational Koopman Models: Slow Collective Variables and
Molecular Kinetics from Short off-Equilibrium Simulations.” The Journal of
Chemical Physics, 154104, 2017, doi:10.1063/1.4979344.'
short: H. Wu, F. Nüske, F. Paul, S. Klus, P. Koltai, F. Noé, The Journal of Chemical
Physics (2017).
date_created: 2021-04-30T16:57:21Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.4979344
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
issn:
- 0021-9606
- 1089-7690
publication_status: published
status: public
title: 'Variational Koopman models: Slow collective variables and molecular kinetics
from short off-equilibrium simulations'
type: journal_article
user_id: '81513'
year: '2017'
...
---
_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: '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: '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: '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: '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: '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: '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: '21937'
article_number: '054105'
author:
- first_name: Feliks
full_name: Nüske, Feliks
id: '81513'
last_name: Nüske
orcid: 0000-0003-2444-7889
- first_name: Reinhold
full_name: Schneider, Reinhold
last_name: Schneider
- first_name: Francesca
full_name: Vitalini, Francesca
last_name: Vitalini
- first_name: Frank
full_name: Noé, Frank
last_name: Noé
citation:
ama: Nüske F, Schneider R, Vitalini F, Noé F. Variational tensor approach for approximating
the rare-event kinetics of macromolecular systems. The Journal of Chemical
Physics. 2016. doi:10.1063/1.4940774
apa: Nüske, F., Schneider, R., Vitalini, F., & Noé, F. (2016). Variational tensor
approach for approximating the rare-event kinetics of macromolecular systems.
The Journal of Chemical Physics. https://doi.org/10.1063/1.4940774
bibtex: '@article{Nüske_Schneider_Vitalini_Noé_2016, title={Variational tensor approach
for approximating the rare-event kinetics of macromolecular systems}, DOI={10.1063/1.4940774}, number={054105},
journal={The Journal of Chemical Physics}, author={Nüske, Feliks and Schneider,
Reinhold and Vitalini, Francesca and Noé, Frank}, year={2016} }'
chicago: Nüske, Feliks, Reinhold Schneider, Francesca Vitalini, and Frank Noé. “Variational
Tensor Approach for Approximating the Rare-Event Kinetics of Macromolecular Systems.”
The Journal of Chemical Physics, 2016. https://doi.org/10.1063/1.4940774.
ieee: F. Nüske, R. Schneider, F. Vitalini, and F. Noé, “Variational tensor approach
for approximating the rare-event kinetics of macromolecular systems,” The Journal
of Chemical Physics, 2016.
mla: Nüske, Feliks, et al. “Variational Tensor Approach for Approximating the Rare-Event
Kinetics of Macromolecular Systems.” The Journal of Chemical Physics, 054105,
2016, doi:10.1063/1.4940774.
short: F. Nüske, R. Schneider, F. Vitalini, F. Noé, The Journal of Chemical Physics
(2016).
date_created: 2021-04-30T16:54:43Z
date_updated: 2022-01-06T06:55:20Z
department:
- _id: '101'
doi: 10.1063/1.4940774
extern: '1'
language:
- iso: eng
publication: The Journal of Chemical Physics
publication_identifier:
issn:
- 0021-9606
- 1089-7690
publication_status: published
status: public
title: Variational tensor approach for approximating the rare-event kinetics of macromolecular
systems
type: journal_article
user_id: '81513'
year: '2016'
...