Learning Koopman-based Stability Certificates for Unknown Nonlinear Systems

• URL: http://arxiv.org/abs/2412.02807v1
• Date: Tue, 03 Dec 2024 20:18:24 GMT
• Title: Learning Koopman-based Stability Certificates for Unknown Nonlinear Systems
• Authors: Ruikun Zhou, Yiming Meng, Zhexuan Zeng, Jun Liu,
• Abstract summary: We propose an algorithmic framework to simultaneously learn the vector field and Lyapunov functions for unknown nonlinear systems. We show that the learned Lyapunov functions can be formally verified using a satisfiability modulo theories (SMT) solver.
• Score: 4.2162963332651575
• License:
• Abstract: 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.

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