Physics-Informed Neural Network Lyapunov Functions: PDE Characterization, Learning, and Verification

Autor:	Liu, Jun, Meng, Yiming, Fitzsimmons, Maxwell, Zhou, Ruikun
Rok vydání:	2023
Předmět:	Mathematics - Optimization and Control Computer Science - Machine Learning Electrical Engineering and Systems Science - Systems and Control
Druh dokumentu:	Working Paper
Popis:	We provide a systematic investigation of using physics-informed neural networks to compute Lyapunov functions. We encode Lyapunov conditions as a partial differential equation (PDE) and use this for training neural network Lyapunov functions. We analyze the analytical properties of the solutions to the Lyapunov and Zubov PDEs. In particular, we show that employing the Zubov equation in training neural Lyapunov functions can lead to approximate regions of attraction close to the true domain of attraction. We also examine approximation errors and the convergence of neural approximations to the unique solution of Zubov's equation. We then provide sufficient conditions for the learned neural Lyapunov functions that can be readily verified by satisfiability modulo theories (SMT) solvers, enabling formal verification of both local stability analysis and region-of-attraction estimates in the large. Through a number of nonlinear examples, ranging from low to high dimensions, we demonstrate that the proposed framework can outperform traditional sums-of-squares (SOS) Lyapunov functions obtained using semidefinite programming (SDP). Comment: The current version has been submitted for publication; corrected some minor typos from v2
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2312.09131 Zobrazit plný text záznamu View this record from Arxiv