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Multiobjective strict dissipativity via a weighted sum approach

Title data

Grüne, Lars ; Krügel, Lisa ; Müller, Matthias A.:
Multiobjective strict dissipativity via a weighted sum approach.
Bayreuth ; Hannover , 2022 . - 19 p.
DOI: https://doi.org/10.48550/arXiv.2207.00373

Official URL: Volltext

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Project information

Project title:
Project's official titleProject's id
Performance Analysis for Distributed and Multiobjective Model Predictive ControlGr 1569/13-2

Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

We consider nonlinear model predictive control (MPC) with multiple competing cost functions. This leads to the formulation of multiobjective optimal control problems (MO OCPs). Since the design of MPC algorithms for directly solving multiobjective problems is rather complicated, particularly if terminal conditions shall be avoided, we use an indirect approach via a weighted sum formulation for solving these MO OCPs. This way, for each set of weights we obtain an optimal control problem with a single objective. In economic MPC it is known that strict dissipativity is the key assumption for concluding performance and stability results. We thus investigate under which conditions a convex combination of strictly dissipative stage costs is strictly dissipative again. We first give conditions for problems with linear dynamics and then move on to consider fully nonlinear optimal control problems. We derive both necessary and sufficient conditions on the individual cost functions and on the weights to conclude strict dissipativity and illustrate our findings with numerical examples.

Further data

Item Type: Preprint, postprint
Refereed: Yes
Keywords: Strict Dissipativity; Multiobjective Optimal Control; Model Predictive Control; Weighted Sum Approach
Institutions of the University: Faculties
Faculties > Faculty of Mathematics, Physics und Computer Science
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics)
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) > Chair Mathematics V (Applied Mathematics) - Univ.-Prof. Dr. Lars Grüne
Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Applied Mathematics
Profile Fields
Profile Fields > Advanced Fields
Profile Fields > Advanced Fields > Nonlinear Dynamics
Research Institutions
Research Institutions > Research Centres
Research Institutions > Research Centres > Forschungszentrum für Modellbildung und Simulation (MODUS)
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 04 Jul 2022 09:17
Last Modified: 04 Jul 2022 09:17
URI: https://eref.uni-bayreuth.de/id/eprint/70379