---
_id: '30733'
abstract:
- lang: eng
text: Hamilton-Jacobi reachability methods for safety-critical control have been
well studied, but the safety guarantees derived rely on the accuracy of the numerical
computation. Thus, it is crucial to understand and account for any inaccuracies
that occur due to uncertainty in the underlying dynamics and environment as well
as the induced numerical errors. To this end, we propose a framework for modeling
the error of the value function inherent in Hamilton-Jacobi reachability using
a Gaussian process. The derived safety controller can be used in conjuncture with
arbitrary controllers to provide a safe hybrid control law. The marginal likelihood
of the Gaussian process then provides a confidence metric used to determine switches
between a least restrictive controller and a safety controller. We test both the
prediction as well as the correction capabilities of the presented method in a
classical pursuit-evasion example.
author:
- first_name: Nikolaus
full_name: Vertovec, Nikolaus
id: '93930'
last_name: Vertovec
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kostas
full_name: Margellos, Kostas
last_name: Margellos
citation:
ama: 'Vertovec N, Ober-Blöbaum S, Margellos K. Verification of safety critical control
policies using kernel methods. In: ; 2022:1870-1875.'
apa: Vertovec, N., Ober-Blöbaum, S., & Margellos, K. (2022). Verification
of safety critical control policies using kernel methods. 1870–1875.
bibtex: '@inproceedings{Vertovec_Ober-Blöbaum_Margellos_2022, title={Verification
of safety critical control policies using kernel methods}, author={Vertovec, Nikolaus
and Ober-Blöbaum, Sina and Margellos, Kostas}, year={2022}, pages={1870–1875}
}'
chicago: Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Verification
of Safety Critical Control Policies Using Kernel Methods,” 1870–75, 2022.
ieee: N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Verification of safety critical
control policies using kernel methods,” London, 2022, pp. 1870–1875.
mla: Vertovec, Nikolaus, et al. Verification of Safety Critical Control Policies
Using Kernel Methods. 2022, pp. 1870–75.
short: 'N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: 2022, pp. 1870–1875.'
conference:
end_date: 2022-07-15
location: London
name: 2022 European Control Conference (ECC)
start_date: 2022-07-12
date_created: 2022-03-31T11:14:13Z
date_updated: 2023-11-29T10:00:18Z
ddc:
- '510'
department:
- _id: '636'
has_accepted_license: '1'
language:
- iso: eng
page: 1870-1875
status: public
title: Verification of safety critical control policies using kernel methods
type: conference
user_id: '15694'
year: '2022'
...
---
_id: '44624'
author:
- first_name: Timm
full_name: Faulwasser, Timm
last_name: Faulwasser
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Manuel
full_name: Schaller, Manuel
last_name: Schaller
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Schaller M, Worthmann K. Manifold
turnpikes, trims, and symmetries. Mathematics of Control, Signals, and Systems.
2022;34:759-788.
apa: Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., Schaller, M., & Worthmann,
K. (2022). Manifold turnpikes, trims, and symmetries. Mathematics of Control,
Signals, and Systems, 34, 759–788.
bibtex: '@article{Faulwasser_Flaßkamp_Ober-Blöbaum_Schaller_Worthmann_2022, title={Manifold
turnpikes, trims, and symmetries}, volume={34}, journal={Mathematics of Control,
Signals, and Systems}, publisher={Springer}, author={Faulwasser, Timm and Flaßkamp,
Kathrin and Ober-Blöbaum, Sina and Schaller, Manuel and Worthmann, Karl}, year={2022},
pages={759–788} }'
chicago: 'Faulwasser, Timm, Kathrin Flaßkamp, Sina Ober-Blöbaum, Manuel Schaller,
and Karl Worthmann. “Manifold Turnpikes, Trims, and Symmetries.” Mathematics
of Control, Signals, and Systems 34 (2022): 759–88.'
ieee: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, and K. Worthmann,
“Manifold turnpikes, trims, and symmetries,” Mathematics of Control, Signals,
and Systems, vol. 34, pp. 759–788, 2022.
mla: Faulwasser, Timm, et al. “Manifold Turnpikes, Trims, and Symmetries.” Mathematics
of Control, Signals, and Systems, vol. 34, Springer, 2022, pp. 759–88.
short: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, M. Schaller, K. Worthmann, Mathematics
of Control, Signals, and Systems 34 (2022) 759–788.
date_created: 2023-05-08T09:04:06Z
date_updated: 2023-05-08T09:04:26Z
department:
- _id: '636'
intvolume: ' 34'
language:
- iso: eng
page: 759-788
publication: Mathematics of Control, Signals, and Systems
publisher: Springer
status: public
title: Manifold turnpikes, trims, and symmetries
type: journal_article
user_id: '15694'
volume: 34
year: '2022'
...
---
_id: '23382'
abstract:
- lang: eng
text: Hamiltonian systems are differential equations which describe systems in classical
mechanics, plasma physics, and sampling problems. They exhibit many structural
properties, such as a lack of attractors and the presence of conservation laws.
To predict Hamiltonian dynamics based on discrete trajectory observations, incorporation
of prior knowledge about Hamiltonian structure greatly improves predictions. This
is typically done by learning the system's Hamiltonian and then integrating the
Hamiltonian vector field with a symplectic integrator. For this, however, Hamiltonian
data needs to be approximated based on the trajectory observations. Moreover,
the numerical integrator introduces an additional discretisation error. In this
paper, we show that an inverse modified Hamiltonian structure adapted to the geometric
integrator can be learned directly from observations. A separate approximation
step for the Hamiltonian data avoided. The inverse modified data compensates for
the discretisation error such that the discretisation error is eliminated. The
technique is developed for Gaussian Processes.
article_type: original
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Offen C, Ober-Blöbaum S. Symplectic integration of learned Hamiltonian systems.
Chaos: An Interdisciplinary Journal of Nonlinear Science. 2022;32(1). doi:10.1063/5.0065913'
apa: 'Offen, C., & Ober-Blöbaum, S. (2022). Symplectic integration of learned
Hamiltonian systems. Chaos: An Interdisciplinary Journal of Nonlinear Science,
32(1). https://doi.org/10.1063/5.0065913'
bibtex: '@article{Offen_Ober-Blöbaum_2022, title={Symplectic integration of learned
Hamiltonian systems}, volume={32(1)}, DOI={10.1063/5.0065913},
journal={Chaos: An Interdisciplinary Journal of Nonlinear Science}, publisher={AIP},
author={Offen, Christian and Ober-Blöbaum, Sina}, year={2022} }'
chicago: 'Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned
Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science
32(1) (2022). https://doi.org/10.1063/5.0065913.'
ieee: 'C. Offen and S. Ober-Blöbaum, “Symplectic integration of learned Hamiltonian
systems,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.
32(1), 2022, doi: 10.1063/5.0065913.'
mla: 'Offen, Christian, and Sina Ober-Blöbaum. “Symplectic Integration of Learned
Hamiltonian Systems.” Chaos: An Interdisciplinary Journal of Nonlinear Science,
vol. 32(1), AIP, 2022, doi:10.1063/5.0065913.'
short: 'C. Offen, S. Ober-Blöbaum, Chaos: An Interdisciplinary Journal of Nonlinear
Science 32(1) (2022).'
date_created: 2021-08-11T08:24:02Z
date_updated: 2023-08-10T08:48:14Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1063/5.0065913
external_id:
arxiv:
- '2108.02492'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2021-12-13T14:56:15Z
date_updated: 2021-12-13T14:56:15Z
file_id: '28734'
file_name: SymplecticShadowIntegration_AIP.pdf
file_size: 2285059
relation: main_file
file_date_updated: 2021-12-13T14:56:15Z
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://aip.scitation.org/doi/abs/10.1063/5.0065913
oa: '1'
publication: 'Chaos: An Interdisciplinary Journal of Nonlinear Science'
publication_status: published
publisher: AIP
quality_controlled: '1'
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Christian-Offen/symplectic-shadow-integration
status: public
title: Symplectic integration of learned Hamiltonian systems
type: journal_article
user_id: '85279'
volume: 32(1)
year: '2022'
...
---
_id: '29421'
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: M.
full_name: Vermeeren, M.
last_name: Vermeeren
citation:
ama: 'Ober-Blöbaum S, Vermeeren M. Superconvergence of galerkin variational integrators.
In: IFAC-PapersOnLine, ed. 7th IIFAC Workshop on Lagrangian and Hamiltonian
Methods for Nonlinear Control LHMNC. Vol 54(19). ; 2021:327-333.'
apa: 'Ober-Blöbaum, S., & Vermeeren, M. (2021). Superconvergence of galerkin
variational integrators. In IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop on
Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC: Vol. 54(19)
(pp. 327–333).'
bibtex: '@inproceedings{Ober-Blöbaum_Vermeeren_2021, title={Superconvergence of
galerkin variational integrators}, volume={54(19)}, booktitle={7th IIFAC Workshop
on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC}, author={Ober-Blöbaum,
Sina and Vermeeren, M.}, editor={IFAC-PapersOnLine}, year={2021}, pages={327–333}
}'
chicago: Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational
Integrators.” In 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, edited by IFAC-PapersOnLine, 54(19):327–33, 2021.
ieee: S. Ober-Blöbaum and M. Vermeeren, “Superconvergence of galerkin variational
integrators,” in 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, 2021, vol. 54(19), pp. 327–333.
mla: Ober-Blöbaum, Sina, and M. Vermeeren. “Superconvergence of Galerkin Variational
Integrators.” 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for
Nonlinear Control LHMNC, edited by IFAC-PapersOnLine, vol. 54(19), 2021, pp.
327–33.
short: 'S. Ober-Blöbaum, M. Vermeeren, in: IFAC-PapersOnLine (Ed.), 7th IIFAC Workshop
on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC, 2021, pp. 327–333.'
corporate_editor:
- IFAC-PapersOnLine
date_created: 2022-01-18T14:27:56Z
date_updated: 2022-01-21T13:36:53Z
department:
- _id: '636'
language:
- iso: eng
page: 327-333
publication: 7th IIFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear
Control LHMNC
status: public
title: Superconvergence of galerkin variational integrators
type: conference
user_id: '15694'
volume: 54(19)
year: '2021'
...
---
_id: '16294'
abstract:
- lang: eng
text: "Model predictive control is a prominent approach to construct a feedback\r\ncontrol
loop for dynamical systems. Due to real-time constraints, the major\r\nchallenge
in MPC is to solve model-based optimal control problems in a very\r\nshort amount
of time. For linear-quadratic problems, Bemporad et al. have\r\nproposed an explicit
formulation where the underlying optimization problems are\r\nsolved a priori
in an offline phase. In this article, we present an extension\r\nof this concept
in two significant ways. We consider nonlinear problems and -\r\nmore importantly
- problems with multiple conflicting objective functions. In\r\nthe offline phase,
we build a library of Pareto optimal solutions from which we\r\nthen obtain a
valid compromise solution in the online phase according to a\r\ndecision maker's
preference. Since the standard multi-parametric programming\r\napproach is no
longer valid in this situation, we instead use interpolation\r\nbetween different
entries of the library. To reduce the number of problems that\r\nhave to be solved
in the offline phase, we exploit symmetries in the dynamical\r\nsystem and the
corresponding multiobjective optimal control problem. The\r\nresults are verified
using two different examples from autonomous driving."
author:
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
citation:
ama: Ober-Blöbaum S, Peitz S. Explicit multiobjective model predictive control for
nonlinear systems with symmetries. International Journal of Robust and Nonlinear
Control. 2021;31(2):380-403. doi:10.1002/rnc.5281
apa: Ober-Blöbaum, S., & Peitz, S. (2021). Explicit multiobjective model predictive
control for nonlinear systems with symmetries. International Journal of Robust
and Nonlinear Control, 31(2), 380–403. https://doi.org/10.1002/rnc.5281
bibtex: '@article{Ober-Blöbaum_Peitz_2021, title={Explicit multiobjective model
predictive control for nonlinear systems with symmetries}, volume={31(2)}, DOI={10.1002/rnc.5281}, journal={International
Journal of Robust and Nonlinear Control}, author={Ober-Blöbaum, Sina and Peitz,
Sebastian}, year={2021}, pages={380–403} }'
chicago: 'Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model
Predictive Control for Nonlinear Systems with Symmetries.” International Journal
of Robust and Nonlinear Control 31(2) (2021): 380–403. https://doi.org/10.1002/rnc.5281.'
ieee: 'S. Ober-Blöbaum and S. Peitz, “Explicit multiobjective model predictive control
for nonlinear systems with symmetries,” International Journal of Robust and
Nonlinear Control, vol. 31(2), pp. 380–403, 2021, doi: 10.1002/rnc.5281.'
mla: Ober-Blöbaum, Sina, and Sebastian Peitz. “Explicit Multiobjective Model Predictive
Control for Nonlinear Systems with Symmetries.” International Journal of Robust
and Nonlinear Control, vol. 31(2), 2021, pp. 380–403, doi:10.1002/rnc.5281.
short: S. Ober-Blöbaum, S. Peitz, International Journal of Robust and Nonlinear
Control 31(2) (2021) 380–403.
date_created: 2020-03-13T12:44:36Z
date_updated: 2022-01-24T13:27:50Z
department:
- _id: '101'
doi: 10.1002/rnc.5281
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://onlinelibrary.wiley.com/doi/epdf/10.1002/rnc.5281
oa: '1'
page: 380-403
project:
- _id: '52'
name: Computing Resources Provided by the Paderborn Center for Parallel Computing
publication: International Journal of Robust and Nonlinear Control
status: public
title: Explicit multiobjective model predictive control for nonlinear systems with
symmetries
type: journal_article
user_id: '15694'
volume: 31(2)
year: '2021'
...
---
_id: '22894'
abstract:
- lang: eng
text: "The first order optimality conditions of optimal control problems (OCPs)
can\r\nbe regarded as boundary value problems for Hamiltonian systems. Variational
or\r\nsymplectic discretisation methods are classically known for their excellent\r\nlong
term behaviour. As boundary value problems are posed on intervals of\r\nfixed,
moderate length, it is not immediately clear whether methods can profit\r\nfrom
structure preservation in this context. When parameters are present,\r\nsolutions
can undergo bifurcations, for instance, two solutions can merge and\r\nannihilate
one another as parameters are varied. We will show that generic\r\nbifurcations
of an OCP are preserved under discretisation when the OCP is\r\neither directly
discretised to a discrete OCP (direct method) or translated\r\ninto a Hamiltonian
boundary value problem using first order necessary\r\nconditions of optimality
which is then solved using a symplectic integrator\r\n(indirect method). Moreover,
certain bifurcations break when a non-symplectic\r\nscheme is used. The general
phenomenon is illustrated on the example of a cut\r\nlocus of an ellipsoid."
author:
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: Offen C, Ober-Blöbaum S. Bifurcation preserving discretisations of optimal
control problems. 2021;54(19):334-339. doi:https://doi.org/10.1016/j.ifacol.2021.11.099
apa: 'Offen, C., & Ober-Blöbaum, S. (2021). Bifurcation preserving discretisations
of optimal control problems: Vol. 54(19) (pp. 334–339). https://doi.org/10.1016/j.ifacol.2021.11.099'
bibtex: '@article{Offen_Ober-Blöbaum_2021, series={IFAC-PapersOnLine}, title={Bifurcation
preserving discretisations of optimal control problems}, volume={54(19)}, DOI={https://doi.org/10.1016/j.ifacol.2021.11.099},
author={Offen, Christian and Ober-Blöbaum, Sina}, year={2021}, pages={334–339},
collection={IFAC-PapersOnLine} }'
chicago: Offen, Christian, and Sina Ober-Blöbaum. “Bifurcation Preserving Discretisations
of Optimal Control Problems.” IFAC-PapersOnLine, 2021. https://doi.org/10.1016/j.ifacol.2021.11.099.
ieee: 'C. Offen and S. Ober-Blöbaum, “Bifurcation preserving discretisations of
optimal control problems,” vol. 54(19). pp. 334–339, 2021, doi: https://doi.org/10.1016/j.ifacol.2021.11.099.'
mla: Offen, Christian, and Sina Ober-Blöbaum. Bifurcation Preserving Discretisations
of Optimal Control Problems. 2021, pp. 334–39, doi:https://doi.org/10.1016/j.ifacol.2021.11.099.
short: C. Offen, S. Ober-Blöbaum, 54(19) (2021) 334–339.
conference:
end_date: 2021-10-13
location: Berlin, Germany
name: 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control,
LHMNC 2021
start_date: 2021-10-11
date_created: 2021-07-29T09:38:32Z
date_updated: 2023-11-29T10:19:41Z
ddc:
- '510'
department:
- _id: '636'
doi: https://doi.org/10.1016/j.ifacol.2021.11.099
external_id:
arxiv:
- '2107.13853'
file:
- access_level: open_access
content_type: application/pdf
creator: coffen
date_created: 2021-07-29T09:37:49Z
date_updated: 2021-07-29T09:37:49Z
file_id: '22895'
file_name: ifacconf.pdf
file_size: 3125220
relation: main_file
file_date_updated: 2021-07-29T09:37:49Z
has_accepted_license: '1'
keyword:
- optimal control
- catastrophe theory
- bifurcations
- variational methods
- symplectic integrators
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.sciencedirect.com/science/article/pii/S2405896321021236
oa: '1'
page: 334-339
publication_identifier:
issn:
- 2405-8963
publication_status: published
quality_controlled: '1'
related_material:
link:
- description: GitHub/Zenodo
relation: software
url: https://doi.org/10.5281/zenodo.4562664
series_title: IFAC-PapersOnLine
status: public
title: Bifurcation preserving discretisations of optimal control problems
type: conference
user_id: '15694'
volume: 54(19)
year: '2021'
...
---
_id: '21572'
author:
- first_name: Steffen
full_name: Ridderbusch, Steffen
last_name: Ridderbusch
- first_name: Christian
full_name: Offen, Christian
id: '85279'
last_name: Offen
orcid: 0000-0002-5940-8057
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Paul
full_name: Goulart, Paul
last_name: Goulart
citation:
ama: 'Ridderbusch S, Offen C, Ober-Blöbaum S, Goulart P. Learning ODE Models with
Qualitative Structure Using Gaussian Processes . In: 2021 60th IEEE Conference
on Decision and Control (CDC). IEEE; 2021:2896. doi:10.1109/CDC45484.2021.9683426'
apa: Ridderbusch, S., Offen, C., Ober-Blöbaum, S., & Goulart, P. (2021). Learning
ODE Models with Qualitative Structure Using Gaussian Processes . 2021 60th
IEEE Conference on Decision and Control (CDC), 2896. https://doi.org/10.1109/CDC45484.2021.9683426
bibtex: '@inproceedings{Ridderbusch_Offen_Ober-Blöbaum_Goulart_2021, title={Learning
ODE Models with Qualitative Structure Using Gaussian Processes }, DOI={10.1109/CDC45484.2021.9683426},
booktitle={2021 60th IEEE Conference on Decision and Control (CDC)}, publisher={IEEE},
author={Ridderbusch, Steffen and Offen, Christian and Ober-Blöbaum, Sina and Goulart,
Paul}, year={2021}, pages={2896} }'
chicago: Ridderbusch, Steffen, Christian Offen, Sina Ober-Blöbaum, and Paul Goulart.
“Learning ODE Models with Qualitative Structure Using Gaussian Processes .” In
2021 60th IEEE Conference on Decision and Control (CDC), 2896. IEEE, 2021.
https://doi.org/10.1109/CDC45484.2021.9683426.
ieee: 'S. Ridderbusch, C. Offen, S. Ober-Blöbaum, and P. Goulart, “Learning ODE
Models with Qualitative Structure Using Gaussian Processes ,” in 2021 60th
IEEE Conference on Decision and Control (CDC), Austin, TX, USA, 2021, p. 2896,
doi: 10.1109/CDC45484.2021.9683426.'
mla: Ridderbusch, Steffen, et al. “Learning ODE Models with Qualitative Structure
Using Gaussian Processes .” 2021 60th IEEE Conference on Decision and Control
(CDC), IEEE, 2021, p. 2896, doi:10.1109/CDC45484.2021.9683426.
short: 'S. Ridderbusch, C. Offen, S. Ober-Blöbaum, P. Goulart, in: 2021 60th IEEE
Conference on Decision and Control (CDC), IEEE, 2021, p. 2896.'
conference:
end_date: 2021-12-17
location: Austin, TX, USA
name: 60th IEEE Conference on Decision and Control (CDC)
start_date: 2021-12-14
date_created: 2021-03-30T10:27:44Z
date_updated: 2023-11-29T10:24:55Z
department:
- _id: '636'
doi: 10.1109/CDC45484.2021.9683426
external_id:
arxiv:
- '2011.05364'
language:
- iso: eng
page: '2896'
publication: 2021 60th IEEE Conference on Decision and Control (CDC)
publication_identifier:
eisbn:
- 978-1-6654-3659-5
publication_status: published
publisher: IEEE
related_material:
link:
- description: GitHub
relation: software
url: https://github.com/Crown421/StructureGPs-paper
status: public
title: 'Learning ODE Models with Qualitative Structure Using Gaussian Processes '
type: conference
user_id: '15694'
year: '2021'
...
---
_id: '21592'
abstract:
- lang: eng
text: We propose a reachability approach for infinite and finite horizon multi-objective
optimization problems for low-thrust spacecraft trajectory design. The main advantage
of the proposed method is that the Pareto front can be efficiently constructed
from the zero level set of the solution to a Hamilton-Jacobi-Bellman equation.
We demonstrate the proposed method by applying it to a low-thrust spacecraft trajectory
design problem. By deriving the analytic expression for the Hamiltonian and the
optimal control policy, we are able to efficiently compute the backward reachable
set and reconstruct the optimal trajectories. Furthermore, we show that any reconstructed
trajectory will be guaranteed to be weakly Pareto optimal. The proposed method
can be used as a benchmark for future research of applying reachability analysis
to low-thrust spacecraft trajectory design.
author:
- first_name: Nikolaus
full_name: Vertovec, Nikolaus
id: '87056'
last_name: Vertovec
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Kostas
full_name: Margellos, Kostas
last_name: Margellos
citation:
ama: 'Vertovec N, Ober-Blöbaum S, Margellos K. Multi-objective minimum time optimal
control for low-thrust trajectory design. In: ; :1975-1980.'
apa: Vertovec, N., Ober-Blöbaum, S., & Margellos, K. (n.d.). Multi-objective
minimum time optimal control for low-thrust trajectory design. 1975–1980.
bibtex: '@inproceedings{Vertovec_Ober-Blöbaum_Margellos, title={Multi-objective
minimum time optimal control for low-thrust trajectory design}, author={Vertovec,
Nikolaus and Ober-Blöbaum, Sina and Margellos, Kostas}, pages={1975–1980} }'
chicago: Vertovec, Nikolaus, Sina Ober-Blöbaum, and Kostas Margellos. “Multi-Objective
Minimum Time Optimal Control for Low-Thrust Trajectory Design,” 1975–80, n.d.
ieee: N. Vertovec, S. Ober-Blöbaum, and K. Margellos, “Multi-objective minimum time
optimal control for low-thrust trajectory design,” Rotterdam, the Netherlands,
pp. 1975–1980.
mla: Vertovec, Nikolaus, et al. Multi-Objective Minimum Time Optimal Control
for Low-Thrust Trajectory Design. pp. 1975–80.
short: 'N. Vertovec, S. Ober-Blöbaum, K. Margellos, in: n.d., pp. 1975–1980.'
conference:
end_date: 2021-07-02
location: Rotterdam, the Netherlands
name: 2021 European Control Conference (ECC)
start_date: 2021-06-29
date_created: 2021-04-03T03:00:35Z
date_updated: 2023-11-29T10:26:49Z
department:
- _id: '636'
external_id:
arxiv:
- '2103.08813'
language:
- iso: eng
page: 1975-1980
publication_status: accepted
status: public
title: Multi-objective minimum time optimal control for low-thrust trajectory design
type: conference
user_id: '15694'
year: '2021'
...
---
_id: '29868'
author:
- first_name: F.
full_name: Jiménez, F.
last_name: Jiménez
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Jiménez F, Ober-Blöbaum S. Fractional Damping Through Restricted Calculus
of Variations. In: Nichtlineare Sci 31. Vol 46. J Nonlinear Sci . ; 2021.'
apa: Jiménez, F., & Ober-Blöbaum, S. (2021). Fractional Damping Through Restricted
Calculus of Variations. Nichtlineare Sci 31, 46.
bibtex: '@inproceedings{Jiménez_Ober-Blöbaum_2021, series={J Nonlinear Sci }, title={Fractional
Damping Through Restricted Calculus of Variations}, volume={46}, booktitle={Nichtlineare
Sci 31}, author={Jiménez, F. and Ober-Blöbaum, Sina}, year={2021}, collection={J
Nonlinear Sci } }'
chicago: Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted
Calculus of Variations.” In Nichtlineare Sci 31, Vol. 46. J Nonlinear Sci
, 2021.
ieee: F. Jiménez and S. Ober-Blöbaum, “Fractional Damping Through Restricted Calculus
of Variations,” in Nichtlineare Sci 31, 2021, vol. 46.
mla: Jiménez, F., and Sina Ober-Blöbaum. “Fractional Damping Through Restricted
Calculus of Variations.” Nichtlineare Sci 31, vol. 46, 2021.
short: 'F. Jiménez, S. Ober-Blöbaum, in: Nichtlineare Sci 31, 2021.'
date_created: 2022-02-17T07:28:47Z
date_updated: 2023-11-29T10:23:46Z
department:
- _id: '636'
intvolume: ' 46'
language:
- iso: eng
publication: Nichtlineare Sci 31
series_title: 'J Nonlinear Sci '
status: public
title: Fractional Damping Through Restricted Calculus of Variations
type: conference
user_id: '15694'
volume: 46
year: '2021'
...
---
_id: '47146'
author:
- first_name: Y.
full_name: Lishkova, Y.
last_name: Lishkova
- first_name: M.
full_name: Cannon, M.
last_name: Cannon
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Lishkova Y, Cannon M, Ober-Blöbaum S. A multirate variational approach to
Nonlinear MPC. In: European Control Conference (ECC), IEEE; 2021.'
apa: Lishkova, Y., Cannon, M., & Ober-Blöbaum, S. (2021). A multirate variational
approach to Nonlinear MPC.
bibtex: '@inproceedings{Lishkova_Cannon_Ober-Blöbaum_2021, title={A multirate variational
approach to Nonlinear MPC}, publisher={European Control Conference (ECC), IEEE},
author={Lishkova, Y. and Cannon, M. and Ober-Blöbaum, Sina}, year={2021} }'
chicago: Lishkova, Y., M. Cannon, and Sina Ober-Blöbaum. “A Multirate Variational
Approach to Nonlinear MPC.” European Control Conference (ECC), IEEE, 2021.
ieee: Y. Lishkova, M. Cannon, and S. Ober-Blöbaum, “A multirate variational approach
to Nonlinear MPC,” 2021.
mla: Lishkova, Y., et al. A Multirate Variational Approach to Nonlinear MPC.
European Control Conference (ECC), IEEE, 2021.
short: 'Y. Lishkova, M. Cannon, S. Ober-Blöbaum, in: European Control Conference
(ECC), IEEE, 2021.'
date_created: 2023-09-21T07:14:57Z
date_updated: 2023-09-21T07:27:30Z
language:
- iso: eng
publisher: European Control Conference (ECC), IEEE
status: public
title: A multirate variational approach to Nonlinear MPC
type: conference
user_id: '15694'
year: '2021'
...
---
_id: '29399'
author:
- first_name: D. J. N.
full_name: Limebeer, D. J. N.
last_name: Limebeer
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: F. H.
full_name: Farshi, F. H.
last_name: Farshi
citation:
ama: Limebeer DJN, Ober-Blöbaum S, Farshi FH. Variational integrators for dissipative
systems. IEEE Transactions on Automatic Control. 2020;65(4):1381-1396.
apa: Limebeer, D. J. N., Ober-Blöbaum, S., & Farshi, F. H. (2020). Variational
integrators for dissipative systems. IEEE Transactions on Automatic Control,
65(4), 1381–1396.
bibtex: '@article{Limebeer_Ober-Blöbaum_Farshi_2020, title={Variational integrators
for dissipative systems}, volume={65(4)}, journal={IEEE Transactions on Automatic
Control}, author={Limebeer, D. J. N. and Ober-Blöbaum, Sina and Farshi, F. H.},
year={2020}, pages={1381–1396} }'
chicago: 'Limebeer, D. J. N., Sina Ober-Blöbaum, and F. H. Farshi. “Variational
Integrators for Dissipative Systems.” IEEE Transactions on Automatic Control
65(4) (2020): 1381–96.'
ieee: D. J. N. Limebeer, S. Ober-Blöbaum, and F. H. Farshi, “Variational integrators
for dissipative systems,” IEEE Transactions on Automatic Control, vol.
65(4), pp. 1381–1396, 2020.
mla: Limebeer, D. J. N., et al. “Variational Integrators for Dissipative Systems.”
IEEE Transactions on Automatic Control, vol. 65(4), 2020, pp. 1381–96.
short: D.J.N. Limebeer, S. Ober-Blöbaum, F.H. Farshi, IEEE Transactions on Automatic
Control 65(4) (2020) 1381–1396.
date_created: 2022-01-18T11:17:25Z
date_updated: 2022-01-21T08:26:46Z
department:
- _id: '636'
language:
- iso: eng
page: 1381-1396
publication: IEEE Transactions on Automatic Control
status: public
title: Variational integrators for dissipative systems
type: journal_article
user_id: '15694'
volume: 65(4)
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: '29398'
author:
- first_name: C. I. O.
full_name: Hernández Castellanos, C. I. O.
last_name: Hernández Castellanos
- first_name: G.
full_name: Schütze, G.
last_name: Schütze
- first_name: J.-Q.
full_name: Sun, J.-Q.
last_name: Sun
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: G.
full_name: Morales-Luna, G.
last_name: Morales-Luna
citation:
ama: Hernández Castellanos CIO, Schütze G, Sun J-Q, Ober-Blöbaum S, Morales-Luna
G. Numerical computation of lightly multi-objective robust optimal solutions by
means of generalized cell mapping. Mathematics. 2020;8(11):1959.
apa: Hernández Castellanos, C. I. O., Schütze, G., Sun, J.-Q., Ober-Blöbaum, S.,
& Morales-Luna, G. (2020). Numerical computation of lightly multi-objective
robust optimal solutions by means of generalized cell mapping. Mathematics,
8(11):1959.
bibtex: '@article{Hernández Castellanos_Schütze_Sun_Ober-Blöbaum_Morales-Luna_2020,
title={Numerical computation of lightly multi-objective robust optimal solutions
by means of generalized cell mapping}, volume={8(11):1959}, journal={Mathematics},
author={Hernández Castellanos, C. I. O. and Schütze, G. and Sun, J.-Q. and Ober-Blöbaum,
Sina and Morales-Luna, G.}, year={2020} }'
chicago: Hernández Castellanos, C. I. O., G. Schütze, J.-Q. Sun, Sina Ober-Blöbaum,
and G. Morales-Luna. “Numerical Computation of Lightly Multi-Objective Robust
Optimal Solutions by Means of Generalized Cell Mapping.” Mathematics 8(11):1959
(2020).
ieee: C. I. O. Hernández Castellanos, G. Schütze, J.-Q. Sun, S. Ober-Blöbaum, and
G. Morales-Luna, “Numerical computation of lightly multi-objective robust optimal
solutions by means of generalized cell mapping,” Mathematics, vol. 8(11):1959,
2020.
mla: Hernández Castellanos, C. I. O., et al. “Numerical Computation of Lightly Multi-Objective
Robust Optimal Solutions by Means of Generalized Cell Mapping.” Mathematics,
vol. 8(11):1959, 2020.
short: C.I.O. Hernández Castellanos, G. Schütze, J.-Q. Sun, S. Ober-Blöbaum, G.
Morales-Luna, Mathematics 8(11):1959 (2020).
date_created: 2022-01-18T11:08:28Z
date_updated: 2022-01-21T09:57:35Z
department:
- _id: '636'
language:
- iso: eng
publication: Mathematics
status: public
title: Numerical computation of lightly multi-objective robust optimal solutions by
means of generalized cell mapping
type: journal_article
user_id: '15694'
volume: 8(11):1959
year: '2020'
...
---
_id: '29422'
author:
- first_name: Y.
full_name: Lishkova, Y.
last_name: Lishkova
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: M.
full_name: Cannon, M.
last_name: Cannon
- first_name: S.
full_name: Leyendecker, S.
last_name: Leyendecker
citation:
ama: 'Lishkova Y, Ober-Blöbaum S, Cannon M, Leyendecker S. A multirate variational
approach to simulation and optimal control for flexible spacecraft. In: Accepted
for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference
- Lake Tahoe. ; 2020.'
apa: Lishkova, Y., Ober-Blöbaum, S., Cannon, M., & Leyendecker, S. (2020). A
multirate variational approach to simulation and optimal control for flexible
spacecraft. Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics
Specialist Conference - Lake Tahoe.
bibtex: '@inproceedings{Lishkova_Ober-Blöbaum_Cannon_Leyendecker_2020, title={A
multirate variational approach to simulation and optimal control for flexible
spacecraft}, booktitle={Accepted for publication in Proceedings of 2020 AAS/AIAA
Astrodynamics Specialist Conference - Lake Tahoe}, author={Lishkova, Y. and Ober-Blöbaum,
Sina and Cannon, M. and Leyendecker, S.}, year={2020} }'
chicago: Lishkova, Y., Sina Ober-Blöbaum, M. Cannon, and S. Leyendecker. “A Multirate
Variational Approach to Simulation and Optimal Control for Flexible Spacecraft.”
In Accepted for Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist
Conference - Lake Tahoe, 2020.
ieee: Y. Lishkova, S. Ober-Blöbaum, M. Cannon, and S. Leyendecker, “A multirate
variational approach to simulation and optimal control for flexible spacecraft,”
2020.
mla: Lishkova, Y., et al. “A Multirate Variational Approach to Simulation and Optimal
Control for Flexible Spacecraft.” Accepted for Publication in Proceedings of
2020 AAS/AIAA Astrodynamics Specialist Conference - Lake Tahoe, 2020.
short: 'Y. Lishkova, S. Ober-Blöbaum, M. Cannon, S. Leyendecker, in: Accepted for
Publication in Proceedings of 2020 AAS/AIAA Astrodynamics Specialist Conference
- Lake Tahoe, 2020.'
date_created: 2022-01-18T14:37:53Z
date_updated: 2022-01-21T13:45:40Z
department:
- _id: '636'
language:
- iso: eng
publication: Accepted for publication in Proceedings of 2020 AAS/AIAA Astrodynamics
Specialist Conference - Lake Tahoe
status: public
title: A multirate variational approach to simulation and optimal control for flexible
spacecraft
type: conference
user_id: '15694'
year: '2020'
...
---
_id: '29423'
author:
- first_name: T.
full_name: Faulwasser, T.
last_name: Faulwasser
- first_name: K.
full_name: Flaßkamp, K.
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: 'K. '
full_name: 'Worthmann, K. '
last_name: Worthmann
citation:
ama: 'Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. A dissipativity characterization
of velocity turnpikes in optimal control problems for mechanical systems. In:
24th International Symposium on Mathematical Theory of Networks and Systems.
; 2020.'
apa: Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., & Worthmann, K. (2020).
A dissipativity characterization of velocity turnpikes in optimal control problems
for mechanical systems. 24th International Symposium on Mathematical Theory
of Networks and Systems.
bibtex: '@inproceedings{Faulwasser_Flaßkamp_Ober-Blöbaum_Worthmann_2020, title={A
dissipativity characterization of velocity turnpikes in optimal control problems
for mechanical systems}, booktitle={24th International Symposium on Mathematical
Theory of Networks and Systems}, author={Faulwasser, T. and Flaßkamp, K. and Ober-Blöbaum,
Sina and Worthmann, K. }, year={2020} }'
chicago: Faulwasser, T., K. Flaßkamp, Sina Ober-Blöbaum, and K. Worthmann. “A Dissipativity
Characterization of Velocity Turnpikes in Optimal Control Problems for Mechanical
Systems.” In 24th International Symposium on Mathematical Theory of Networks
and Systems, 2020.
ieee: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “A dissipativity
characterization of velocity turnpikes in optimal control problems for mechanical
systems,” 2020.
mla: Faulwasser, T., et al. “A Dissipativity Characterization of Velocity Turnpikes
in Optimal Control Problems for Mechanical Systems.” 24th International Symposium
on Mathematical Theory of Networks and Systems, 2020.
short: 'T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: 24th International
Symposium on Mathematical Theory of Networks and Systems, 2020.'
date_created: 2022-01-18T14:42:07Z
date_updated: 2022-01-21T13:46:57Z
department:
- _id: '636'
language:
- iso: eng
publication: 24th International Symposium on Mathematical Theory of Networks and Systems
status: public
title: A dissipativity characterization of velocity turnpikes in optimal control problems
for mechanical systems
type: conference
user_id: '15694'
year: '2020'
...
---
_id: '29424'
author:
- first_name: 'J. '
full_name: 'Cresson, J. '
last_name: Cresson
- first_name: F.
full_name: Jiménez, F.
last_name: Jiménez
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
citation:
ama: 'Cresson J, Jiménez F, Ober-Blöbaum S. Modelling of the convection-diffusion
equation through fractional restricted calculus of variations. In: 24th International
Symposium on Mathematical Theory of Networks and Systems. ; 2020.'
apa: Cresson, J., Jiménez, F., & Ober-Blöbaum, S. (2020). Modelling of the convection-diffusion
equation through fractional restricted calculus of variations. 24th International
Symposium on Mathematical Theory of Networks and Systems.
bibtex: '@inproceedings{Cresson_Jiménez_Ober-Blöbaum_2020, title={Modelling of the
convection-diffusion equation through fractional restricted calculus of variations},
booktitle={24th International Symposium on Mathematical Theory of Networks and
Systems}, author={Cresson, J. and Jiménez, F. and Ober-Blöbaum, Sina}, year={2020}
}'
chicago: Cresson, J. , F. Jiménez, and Sina Ober-Blöbaum. “Modelling of the Convection-Diffusion
Equation through Fractional Restricted Calculus of Variations.” In 24th International
Symposium on Mathematical Theory of Networks and Systems, 2020.
ieee: J. Cresson, F. Jiménez, and S. Ober-Blöbaum, “Modelling of the convection-diffusion
equation through fractional restricted calculus of variations,” 2020.
mla: Cresson, J., et al. “Modelling of the Convection-Diffusion Equation through
Fractional Restricted Calculus of Variations.” 24th International Symposium
on Mathematical Theory of Networks and Systems, 2020.
short: 'J. Cresson, F. Jiménez, S. Ober-Blöbaum, in: 24th International Symposium
on Mathematical Theory of Networks and Systems, 2020.'
date_created: 2022-01-18T14:45:22Z
date_updated: 2022-01-21T13:47:49Z
department:
- _id: '636'
language:
- iso: eng
publication: 24th International Symposium on Mathematical Theory of Networks and Systems
status: public
title: Modelling of the convection-diffusion equation through fractional restricted
calculus of variations
type: conference
user_id: '15694'
year: '2020'
...
---
_id: '29413'
author:
- first_name: K.
full_name: Flaßkamp, K.
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: 'S. '
full_name: 'Peitz, S. '
last_name: Peitz
citation:
ama: 'Flaßkamp K, Ober-Blöbaum S, Peitz S. Symmetry in optimal control: A multiobjective
model predictive control approach. In: Junge O, Schütze O, Froyland G, Ober-Blöbaum
S, Padberg-Gehle K, eds. Advances in Dynamics, Optimization and Computation.
Springer International Publishing; 2020:209-237.'
apa: 'Flaßkamp, K., Ober-Blöbaum, S., & Peitz, S. (2020). Symmetry in optimal
control: A multiobjective model predictive control approach. In O. Junge, O. Schütze,
G. Froyland, S. Ober-Blöbaum, & K. Padberg-Gehle (Eds.), Advances in Dynamics,
Optimization and Computation (pp. 209–237). Springer International Publishing.'
bibtex: '@inbook{Flaßkamp_Ober-Blöbaum_Peitz_2020, place={Cham}, title={Symmetry
in optimal control: A multiobjective model predictive control approach}, booktitle={Advances
in Dynamics, Optimization and Computation}, publisher={Springer International
Publishing}, author={Flaßkamp, K. and Ober-Blöbaum, Sina and Peitz, S. }, editor={Junge,
Oliver and Schütze, Oliver and Froyland, Gary and Ober-Blöbaum, Sina and Padberg-Gehle,
Kathrin}, year={2020}, pages={209–237} }'
chicago: 'Flaßkamp, K., Sina Ober-Blöbaum, and S. Peitz. “Symmetry in Optimal Control:
A Multiobjective Model Predictive Control Approach.” In Advances in Dynamics,
Optimization and Computation, edited by Oliver Junge, Oliver Schütze, Gary
Froyland, Sina Ober-Blöbaum, and Kathrin Padberg-Gehle, 209–37. Cham: Springer
International Publishing, 2020.'
ieee: 'K. Flaßkamp, S. Ober-Blöbaum, and S. Peitz, “Symmetry in optimal control:
A multiobjective model predictive control approach,” in Advances in Dynamics,
Optimization and Computation, O. Junge, O. Schütze, G. Froyland, S. Ober-Blöbaum,
and K. Padberg-Gehle, Eds. Cham: Springer International Publishing, 2020, pp.
209–237.'
mla: 'Flaßkamp, K., et al. “Symmetry in Optimal Control: A Multiobjective Model
Predictive Control Approach.” Advances in Dynamics, Optimization and Computation,
edited by Oliver Junge et al., Springer International Publishing, 2020, pp. 209–37.'
short: 'K. Flaßkamp, S. Ober-Blöbaum, S. Peitz, in: O. Junge, O. Schütze, G. Froyland,
S. Ober-Blöbaum, K. Padberg-Gehle (Eds.), Advances in Dynamics, Optimization and
Computation, Springer International Publishing, Cham, 2020, pp. 209–237.'
date_created: 2022-01-18T12:58:18Z
date_updated: 2023-11-08T08:15:14Z
department:
- _id: '636'
editor:
- first_name: Oliver
full_name: Junge, Oliver
last_name: Junge
- first_name: Oliver
full_name: Schütze, Oliver
last_name: Schütze
- first_name: Gary
full_name: Froyland, Gary
last_name: Froyland
- first_name: Sina
full_name: Ober-Blöbaum, Sina
last_name: Ober-Blöbaum
- first_name: Kathrin
full_name: Padberg-Gehle, Kathrin
last_name: Padberg-Gehle
language:
- iso: eng
page: 209-237
place: Cham
publication: Advances in Dynamics, Optimization and Computation
publisher: Springer International Publishing
status: public
title: 'Symmetry in optimal control: A multiobjective model predictive control approach'
type: book_chapter
user_id: '15694'
year: '2020'
...
---
_id: '19993'
author:
- first_name: Kathrin
full_name: Flaßkamp, Kathrin
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: Flaßkamp K, Ober-Blöbaum S, Worthmann K. Symmetry and motion primitives in
model predictive control. MCSS. 2019;31:455-485.
apa: Flaßkamp, K., Ober-Blöbaum, S., & Worthmann, K. (2019). Symmetry and motion
primitives in model predictive control. MCSS, 31, 455–485.
bibtex: '@article{Flaßkamp_Ober-Blöbaum_Worthmann_2019, title={Symmetry and motion
primitives in model predictive control}, volume={31}, journal={MCSS}, author={Flaßkamp,
Kathrin and Ober-Blöbaum, Sina and Worthmann, Karl}, year={2019}, pages={455–485}
}'
chicago: 'Flaßkamp, Kathrin, Sina Ober-Blöbaum, and Karl Worthmann. “Symmetry and
Motion Primitives in Model Predictive Control.” MCSS 31 (2019): 455–85.'
ieee: K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “Symmetry and motion primitives
in model predictive control,” MCSS, vol. 31, pp. 455–485, 2019.
mla: Flaßkamp, Kathrin, et al. “Symmetry and Motion Primitives in Model Predictive
Control.” MCSS, vol. 31, 2019, pp. 455–85.
short: K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, MCSS 31 (2019) 455–485.
date_created: 2020-10-13T18:37:24Z
date_updated: 2022-01-21T10:14:19Z
intvolume: ' 31'
language:
- iso: eng
page: 455-485
publication: MCSS
status: public
title: Symmetry and motion primitives in model predictive control
type: journal_article
user_id: '15694'
volume: 31
year: '2019'
...
---
_id: '29867'
author:
- first_name: Tim
full_name: Faulwasser, Tim
last_name: Faulwasser
- first_name: K.
full_name: Flaßkamp, K.
last_name: Flaßkamp
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Karl
full_name: Worthmann, Karl
last_name: Worthmann
citation:
ama: 'Faulwasser T, Flaßkamp K, Ober-Blöbaum S, Worthmann K. Towards velocity turnpikes
in optimal control of mechanical systems. In: IFAC-PapersOnLine, ed. Vol 52(16).
; 2019:490-495.'
apa: 'Faulwasser, T., Flaßkamp, K., Ober-Blöbaum, S., & Worthmann, K. (2019).
Towards velocity turnpikes in optimal control of mechanical systems: Vol. 52(16)
(IFAC-PapersOnLine, Ed.; pp. 490–495).'
bibtex: '@inproceedings{Faulwasser_Flaßkamp_Ober-Blöbaum_Worthmann_2019, title={Towards
velocity turnpikes in optimal control of mechanical systems}, volume={52(16)},
author={Faulwasser, Tim and Flaßkamp, K. and Ober-Blöbaum, Sina and Worthmann,
Karl}, editor={IFAC-PapersOnLine}, year={2019}, pages={490–495} }'
chicago: Faulwasser, Tim, K. Flaßkamp, Sina Ober-Blöbaum, and Karl Worthmann. “Towards
Velocity Turnpikes in Optimal Control of Mechanical Systems.” edited by IFAC-PapersOnLine,
52(16):490–95, 2019.
ieee: T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, and K. Worthmann, “Towards velocity
turnpikes in optimal control of mechanical systems,” 2019, vol. 52(16), pp. 490–495.
mla: Faulwasser, Tim, et al. Towards Velocity Turnpikes in Optimal Control of
Mechanical Systems. Edited by IFAC-PapersOnLine, vol. 52(16), 2019, pp. 490–95.
short: 'T. Faulwasser, K. Flaßkamp, S. Ober-Blöbaum, K. Worthmann, in: IFAC-PapersOnLine
(Ed.), 2019, pp. 490–495.'
corporate_editor:
- IFAC-PapersOnLine
date_created: 2022-02-17T07:23:52Z
date_updated: 2023-11-08T08:09:01Z
department:
- _id: '636'
language:
- iso: eng
page: 490-495
status: public
title: Towards velocity turnpikes in optimal control of mechanical systems
type: conference
user_id: '15694'
volume: 52(16)
year: '2019'
...
---
_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'
...