In this talk, we first recap the extended Dynamic Mode Decomposition (EDMD) as a very popular datadriven method to predict quantities of interest along the flow of a dynamical control system. To this end, the nonlinear dynamics are lifted into a high-, but finite-dimensional space, on which the surrogate model evolves linearly [1]. We embed EDMD in the Koopman framework to provide a rigorous error analysis depending on the amount of data by splitting up the approximation error into its two sources: projection and estimation [2]. Then, we provide a glimpse into a potential extension towards kernel EDMD (kEDMD). Here, we briefly touch upon the invariance of the respective reproducing kernel Hilbert space (RKHS) under the Koopman flow and the first uniform error bounds [3] for kEDMD. Finally, we present the usefulness of the EDMDbased surrogate model for (predictive) control and present novel results on closed-loop guarantees [3,4].

[1] M.O. Williams, I.G. Kevrekidis, and C. Rowley: A data–driven approximation of the Koopman operator:
Extending dynamic mode decomposition. Journal of Nonlinear Science, 25, 1307-1346, 2015
[2] F. Nüske, S. Peitz, F.M. Philipp, M. Schaller, and K. Worthmann: Finite-data error bounds for Koopmanbased
prediction and control. Journal of Nonlinear Science, 33(1):14, 2023
[3] F. Köhne, F.M. Philipp, M. Schaller, A. Schiela, and K. Worthmann: L^\infty-error bounds for approximations
of the Koopman operator by kernel extended dynamic mode decomposition. arXiv preprint arXiv:2403.18809
[4] L. Bold, L. Grüne, M. Schaller, and K. Worthmann: Practical asymptotic stability of data-driven model
predictive control using extended DMD. arXiv preprint arXiv:2308.00296
[5] R. Strässer, M. Schaller, K. Worthmann, J. Berberich, and F. Allgöwer: SafEDMD: A certified learning
architecture tailored to data-driven control of nonlinear dynamical systems, arXiv preprint arXiv:2402.03145

Referent: Prof. Dr. Karl Worthmann, Universität Ilmenau

Der Vortrag findet um 17.15 Uhr im Raum 210 des Mathematik-Gebäudes 48 statt.

Studierende, Doktorandinnen und Doktoranden sowie Wissenschaftlerinnen und Wissenschaftler des Fachbereichs Mathematik der RPTU und des Fraunhofer ITWM sind herzlich zum Kolloquium eingeladen!