Felix Klein Colloquium: Data-driven approximation of nonlinear dynamical systems in the Koopman framework: prediction and control

In this talk, we first recap the extended Dynamic Mode Decomposition (EDMD) as a very popular data-driven 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. 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. 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 for kEDMD. Finally, we present the usefulness of the EDMD-based surrogate model for (predictive) control and present novel results on closed-loop guarantees.

Speaker: Prof. Dr. Karl Worthmann, TU Ilmenau

Time: 17:15 - 18:30 o'clock

Place: Building 48, room 210

The lectures of the Felix Klein Colloquium will be held at 17:15 in room 210 of the Mathematics Building 48. Beforehand - from 16:45 - there will be an opportunity to meet the speaker at the colloquium tea in room 580.