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Data-driven MPC with stability guarantees using extended dynamic mode decomposition

Title data

Bold, Lea ; Grüne, Lars ; Schaller, Manuel ; Worthmann, Karl:
Data-driven MPC with stability guarantees using extended dynamic mode decomposition.
In: IEEE Transactions on Automatic Control. Vol. Online First (July 2024) . - pp. 1-8.
ISSN 1558-2523
DOI: https://doi.org/10.1109/TAC.2024.3431169

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Project information

Project title:
Project's official title
Project's id
Optimierungsbasierte Steuerung und Regelung
507037103
Project financing: Deutsche Forschungsgemeinschaft

Abstract in another language

For nonlinear (control) systems, extended dynamic mode decomposition (EDMD) is a popular method to obtain data-driven surrogate models. Its theoretical foundation is the Koopman framework, in which one propagates observable functions of the state to obtain a linear representation in an infinite-dimensional space. In this work, we prove practical asymptotic stability of a (controlled) equilibrium for EDMD-based model predictive control, in which the optimization step is conducted using the data-based surrogate model. To this end, we derive novel bounds on the estimation error that are proportional to the norm of state and control. This enables us to show that, if the underlying system is cost controllable, this stabilizablility property is preserved. We conduct numerical simulations illustrating the proven practical asymptotic stability.

Further data

Item Type: Article in a journal
Refereed: Yes
Keywords: model predictive control; stability; data-driven; dynamic mode decomposition; cost controllability
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 > Central research institutes
Research Institutions > Central research institutes > Bayreuth Research Center for Modeling and Simulation - MODUS
Result of work at the UBT: Yes
DDC Subjects: 500 Science > 510 Mathematics
Date Deposited: 26 Jul 2024 08:42
Last Modified: 26 Jul 2024 08:42
URI: https://eref.uni-bayreuth.de/id/eprint/90102

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