---
_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 Since the standard multi-parametric programming\r\napproach is no
longer valid in this situation, we instead use interpolation\r\nbetween different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: '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: '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: '8756'
abstract:
- lang: eng
text: We present a new algorithm for model predictive control of non-linear systems
with respect to multiple, conflicting objectives. The idea is to provide a possibility
to change the objective in real-time, e.g. as a reaction to changes in the environment
or the system state itself. The algorithm utilises elements from various well-established
concepts, namely multiobjective optimal control, economic as well as explicit
model predictive control and motion planning with motion primitives. In order
to realise real-time applicability, we split the computation into an online and
an offline phase and we utilise symmetries in the open-loop optimal control problem
to reduce the number of multiobjective optimal control problems that need to be
solved in the offline phase. The results are illustrated using the example of
an electric vehicle where the longitudinal dynamics are controlled with respect
to the concurrent objectives arrival time and energy consumption.
article_type: original
author:
- first_name: Sebastian
full_name: Peitz, Sebastian
id: '47427'
last_name: Peitz
orcid: https://orcid.org/0000-0002-3389-793X
- first_name: Kai
full_name: Schäfer, Kai
last_name: Schäfer
- first_name: Sina
full_name: Ober-Blöbaum, Sina
id: '16494'
last_name: Ober-Blöbaum
- first_name: Julian
full_name: Eckstein, Julian
last_name: Eckstein
- first_name: Ulrich
full_name: Köhler, Ulrich
last_name: Köhler
- first_name: Michael
full_name: Dellnitz, Michael
last_name: Dellnitz
citation:
ama: Peitz S, Schäfer K, Ober-Blöbaum S, Eckstein J, Köhler U, Dellnitz M. A multiobjective
MPC approach for autonomously driven electric vehicles. Proceedings of the
20th World Congress of the International Federation of Automatic Control (IFAC).
2017;50(1):8674-8679. doi:10.1016/j.ifacol.2017.08.1526
apa: Peitz, S., Schäfer, K., Ober-Blöbaum, S., Eckstein, J., Köhler, U., & Dellnitz,
M. (2017). A multiobjective MPC approach for autonomously driven electric vehicles.
Proceedings of the 20th World Congress of the International Federation of Automatic
Control (IFAC), 50(1), 8674–8679. https://doi.org/10.1016/j.ifacol.2017.08.1526
bibtex: '@article{Peitz_Schäfer_Ober-Blöbaum_Eckstein_Köhler_Dellnitz_2017, title={A
multiobjective MPC approach for autonomously driven electric vehicles}, volume={50},
DOI={10.1016/j.ifacol.2017.08.1526},
number={1}, journal={Proceedings of the 20th World Congress of the International
Federation of Automatic Control (IFAC)}, author={Peitz, Sebastian and Schäfer,
Kai and Ober-Blöbaum, Sina and Eckstein, Julian and Köhler, Ulrich and Dellnitz,
Michael}, year={2017}, pages={8674–8679} }'
chicago: 'Peitz, Sebastian, Kai Schäfer, Sina Ober-Blöbaum, Julian Eckstein, Ulrich
Köhler, and Michael Dellnitz. “A Multiobjective MPC Approach for Autonomously
Driven Electric Vehicles.” Proceedings of the 20th World Congress of the International
Federation of Automatic Control (IFAC) 50, no. 1 (2017): 8674–79. https://doi.org/10.1016/j.ifacol.2017.08.1526.'
ieee: 'S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, and M. Dellnitz,
“A multiobjective MPC approach for autonomously driven electric vehicles,” Proceedings
of the 20th World Congress of the International Federation of Automatic Control
(IFAC), vol. 50, no. 1, pp. 8674–8679, 2017, doi: 10.1016/j.ifacol.2017.08.1526.'
mla: Peitz, Sebastian, et al. “A Multiobjective MPC Approach for Autonomously Driven
Electric Vehicles.” Proceedings of the 20th World Congress of the International
Federation of Automatic Control (IFAC), vol. 50, no. 1, 2017, pp. 8674–79,
doi:10.1016/j.ifacol.2017.08.1526.
short: S. Peitz, K. Schäfer, S. Ober-Blöbaum, J. Eckstein, U. Köhler, M. Dellnitz,
Proceedings of the 20th World Congress of the International Federation of Automatic
Control (IFAC) 50 (2017) 8674–8679.
conference:
end_date: 2017-07-14
start_date: 2017-07-09
date_created: 2019-03-29T13:32:46Z
date_updated: 2022-01-21T13:58:41Z
department:
- _id: '101'
doi: 10.1016/j.ifacol.2017.08.1526
intvolume: ' 50'
issue: '1'
language:
- iso: eng
page: 8674-8679
publication: Proceedings of the 20th World Congress of the International Federation
of Automatic Control (IFAC)
publication_identifier:
issn:
- 2405-8963
publication_status: published
status: public
title: A multiobjective MPC approach for autonomously driven electric vehicles
type: journal_article
user_id: '15694'
volume: 50
year: '2017'
...