---
_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: '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: '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: '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: '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'
...
---
_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: '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: 2024-10-01T13:37:43Z
department:
- _id: '101'
doi: 10.1137/19m1247139
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/epdf/10.1137/19M1247139
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: '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: '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: '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: '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: '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: '16708'
abstract:
- lang: eng
text: " In this work we extend the novel framework developed by Dellnitz, Hessel-von
Molo, and Ziessler to\r\nthe computation of finite dimensional unstable manifolds
of infinite dimensional dynamical systems.\r\nTo this end, we adapt a set-oriented
continuation technique developed by Dellnitz and Hohmann for\r\nthe computation
of such objects of finite dimensional systems with the results obtained in the
work\r\nof Dellnitz, Hessel-von Molo, and Ziessler. We show how to implement this
approach for the analysis\r\nof partial differential equations and illustrate
its feasibility by computing unstable manifolds of the\r\none-dimensional Kuramoto--Sivashinsky
equation as well as for the Mackey--Glass delay differential\r\nequation.\r\n"
author:
- first_name: Adrian
full_name: Ziessler, Adrian
last_name: Ziessler
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
- first_name: Raphael
full_name: Gerlach, Raphael
id: '32655'
last_name: Gerlach
citation:
ama: Ziessler A, Dellnitz M, Gerlach R. The Numerical Computation of Unstable Manifolds
for Infinite Dimensional Dynamical Systems by Embedding Techniques. SIAM Journal
on Applied Dynamical Systems. 2019;18(3):1265-1292. doi:10.1137/18m1204395
apa: Ziessler, A., Dellnitz, M., & Gerlach, R. (2019). The Numerical Computation
of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding
Techniques. SIAM Journal on Applied Dynamical Systems, 18(3), 1265–1292.
https://doi.org/10.1137/18m1204395
bibtex: '@article{Ziessler_Dellnitz_Gerlach_2019, title={The Numerical Computation
of Unstable Manifolds for Infinite Dimensional Dynamical Systems by Embedding
Techniques}, volume={18}, DOI={10.1137/18m1204395},
number={3}, journal={SIAM Journal on Applied Dynamical Systems}, author={Ziessler,
Adrian and Dellnitz, Michael and Gerlach, Raphael}, year={2019}, pages={1265–1292}
}'
chicago: 'Ziessler, Adrian, Michael Dellnitz, and Raphael Gerlach. “The Numerical
Computation of Unstable Manifolds for Infinite Dimensional Dynamical Systems by
Embedding Techniques.” SIAM Journal on Applied Dynamical Systems 18, no.
3 (2019): 1265–92. https://doi.org/10.1137/18m1204395.'
ieee: 'A. Ziessler, M. Dellnitz, and R. Gerlach, “The Numerical Computation of Unstable
Manifolds for Infinite Dimensional Dynamical Systems by Embedding Techniques,”
SIAM Journal on Applied Dynamical Systems, vol. 18, no. 3, pp. 1265–1292,
2019, doi: 10.1137/18m1204395.'
mla: Ziessler, Adrian, et al. “The Numerical Computation of Unstable Manifolds for
Infinite Dimensional Dynamical Systems by Embedding Techniques.” SIAM Journal
on Applied Dynamical Systems, vol. 18, no. 3, 2019, pp. 1265–92, doi:10.1137/18m1204395.
short: A. Ziessler, M. Dellnitz, R. Gerlach, SIAM Journal on Applied Dynamical Systems
18 (2019) 1265–1292.
date_created: 2020-04-16T14:04:20Z
date_updated: 2023-11-17T13:13:09Z
department:
- _id: '101'
doi: 10.1137/18m1204395
intvolume: ' 18'
issue: '3'
language:
- iso: eng
main_file_link:
- url: https://epubs.siam.org/doi/epdf/10.1137/18M1204395
page: 1265-1292
publication: SIAM Journal on Applied Dynamical Systems
publication_identifier:
issn:
- 1536-0040
publication_status: published
status: public
title: The Numerical Computation of Unstable Manifolds for Infinite Dimensional Dynamical
Systems by Embedding Techniques
type: journal_article
user_id: '32655'
volume: 18
year: '2019'
...
---
_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: 2024-09-24T12:09:27Z
ddc:
- '510'
department:
- _id: '101'
external_id:
arxiv:
- '1902.08824'
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: '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: '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: '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: '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: '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: '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'
...