Learning Koopman-based Stability Certificates for Unknown Nonlinear Systems

Autor:	Zhou, Ruikun, Meng, Yiming, Zeng, Zhexuan, Liu, Jun
Rok vydání:	2024
Předmět:	Electrical Engineering and Systems Science - Systems and Control Computer Science - Machine Learning Mathematics - Dynamical Systems
Druh dokumentu:	Working Paper
Popis:	Koopman operator theory has gained significant attention in recent years for identifying discrete-time nonlinear systems by embedding them into an infinite-dimensional linear vector space. However, providing stability guarantees while learning the continuous-time dynamics, especially under conditions of relatively low observation frequency, remains a challenge within the existing Koopman-based learning frameworks. To address this challenge, we propose an algorithmic framework to simultaneously learn the vector field and Lyapunov functions for unknown nonlinear systems, using a limited amount of data sampled across the state space and along the trajectories at a relatively low sampling frequency. The proposed framework builds upon recently developed high-accuracy Koopman generator learning for capturing transient system transitions and physics-informed neural networks for training Lyapunov functions. We show that the learned Lyapunov functions can be formally verified using a satisfiability modulo theories (SMT) solver and provide less conservative estimates of the region of attraction compared to existing methods. Comment: Submitted to L4DC 2025
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.02807 Zobrazit plný text záznamu View this record from Arxiv