Data-driven predictive control with guarantees exemplified in the Koopman framework (Prof. Worthmann, Technische Universität Ilmenau, Germany)

Systems & Control Seminar

• Dienstag, 24.02.2026, 16:00 Uhr
• Raum A145, Gebäude 3403, Appelstr. 11

Abstract

We analyse nonlinear model predictive control (MPC) using data-driven surrogate models in the optimization step. First, we establish asymptotic stability of the origin w.r.t. the MPC closed loop without stabilizing terminal conditions [3]. To this end, we prove that cost controllability of the original system is preserved if sufficiently accurate proportional bounds on the approximation error hold. Second, we exemplarily verify the imposed assumptions for data-driven surrogates generated with kernel extended dynamic mode decomposition (kernel EDMD) based on Koopman operator theory [4]. Hereby, we do not impose invariance assumptions on finite dictionaries, but rather derive all conditions under non-restrictive conditions [2, 1]. Finally, we demonstrate our findings with numerical simulations.

References

1. L. Bold, F. M. Philipp, M. Schaller, and K. Worthmann. Kernel-based Koopman approximants for control: Flexible sampling, error analysis, and stability. SIAM Journal on Control and Optimization, 63(6):4044–4071, 2025.
2. F. Köhne, F. M. Philipp, M. Schaller, A. Schiela, and K. Worthmann. L∞ - error bounds for approximations of the Koopman operator by kernel extended dynamic mode decomposition. SIAM Journal on Applied Dynamical Systems, 24(1):501–529, 2025.
3. I. Schimperna, K. Worthmann, M. Schaller, L. Bold, and L. Magni. Data-driven model predictive control: Asymptotic stability despite approximation errors exemplified in the Koopman framework, 2025. arXiv:2505.05951.
4. R. Strässer, K. Worthmann, I. Mezić, J. Berberich, M. Schaller, and F. Allgöwer. An overview of Koopman-based control: From error bounds to closed-loop guarantees. Annual Reviews in Control, 61:101035, 2026.

Biographical information

Karl Worthmann received his Ph.D. degree in mathematics from the University of Bayreuth, Germany, in 2012. 2019 he be-
came full professor after receiving the Heisenberg-professorship ”Optimization-based Control” by the German Research Foundation (DFG). He was stipend of the German National Academic Foundation. 2013 he has been appointed Junior Fellow of the Society of Applied Mathematics and Mechanics (GAMM), where he served as speaker in 2014 and 2015. His current research interests include systems and control theory with a focus on nonlinear model predictive control, stability analysis, and data-driven control.