Modularized data-driven approximation of the Koopman operator and generator

Autor:	Guo, Yang, Schaller, Manuel, Worthmann, Karl, Streif, Stefan
Rok vydání:	2024
Předmět:	Electrical Engineering and Systems Science - Systems and Control Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	Extended Dynamic Mode Decomposition (EDMD) is a widely-used data-driven approach to learn an approximation of the Koopman operator. Consequently, it provides a powerful tool for data-driven analysis, prediction, and control of nonlinear dynamical (control) systems. In this work, we propose a novel modularized EDMD scheme tailored to interconnected systems. To this end, we utilize the structure of the Koopman generator that allows to learn the dynamics of subsystems individually and thus alleviates the curse of dimensionality by considering observable functions on smaller state spaces. Moreover, our approach canonically enables transfer learning if a system encompasses multiple copies of a model as well as efficient adaption to topology changes without retraining. We provide finite-data bounds on the estimation error using tools from graph theory. The efficacy of the method is illustrated by means of various numerical examples. Comment: 31 pages, 11 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.12277 Zobrazit plný text záznamu View this record from Arxiv