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Practical asymptotic stability of data-driven model predictive control using extended DMD

Title data

Bold, Lea ; Grüne, Lars ; Schaller, Manuel ; Worthmann, Karl:
Practical asymptotic stability of data-driven model predictive control using extended DMD.
Ilmenau ; Bayreuth , 2023 . - 24 p.
DOI: https://doi.org/10.48550/arXiv.2308.00296

Abstract in another language

The extended Dynamic Mode Decomposition (eDMD) is a very popular method to obtain data-driven surrogate models for nonlinear (control) systems governed by ordinary and stochastic differential equations. 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 error bounds that converge to zero if the state approaches the desired equilibrium. Further, we show that, if the underlying system is cost controllable, then this stabilizablility property is preserved. We conduct numerical simulations, which illustrate the proven practical asymptotic stability.

Further data

Item Type: Preprint, postprint
Refereed: Yes
Keywords: data-driven control; model predictive control; robust stability
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: 03 Aug 2023 10:48
Last Modified: 09 Jan 2024 13:50
URI: https://eref.uni-bayreuth.de/id/eprint/86465