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Data-Driven MPC With Stability Guarantees Using Extended Dynamic Mode Decomposition

Name: Data-Driven MPC With Stability Guarantees Using Extended Dynamic Mode Decomposition
Keywords: Optimization and Control (math.OC), FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Systems and Control (eess.SY), Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2025Embargo end date: 01 Jan 2023Publisher:Institute of Electrical and Electronics Engineers (IEEE)Journal:IEEE Transactions on Automatic Control, volume 70, pages 534-541 (issn: 0018-9286, eissn: 2334-3303,

Authors: Lea Bold; Lars Grüne; Manuel Schaller; Karl Worthmann;

doi: 10.1109/tac.2024.3431169 , 10.48550/arxiv.2308.00296

arXiv: http://arxiv.org/abs/2308.00296

Data-Driven MPC With Stability Guarantees Using Extended Dynamic Mode Decomposition

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Abstract

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.

18 pages, 3 figures

Related Organizations

University of Bayreuth
Germany
University of Bayereuth
Germany

Keywords

Optimization and Control (math.OC), FOS: Mathematics, FOS: Electrical engineering, electronic engineering, information engineering, Systems and Control (eess.SY), Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control

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