Learning Region of Attraction for Nonlinear Systems
Abstract
Estimating the region of attraction (ROA) of general nonlinear autonomous systems remains a challenging problem and requires a case-by-case analysis. Leveraging the universal approximation property of neural networks, in this paper, we propose a counterexample-guided method to estimate the ROA of general nonlinear dynamical systems provided that they can be approximated by piecewise linear neural networks and that the approximation error can be bounded. Specifically, our method searches for robust Lyapunov functions using counterexamples, i.e., the states at which the Lyapunov conditions fail. We generate the counterexamples using Mixed-Integer Quadratic Programming. Our method is guaranteed to find a robust Lyapunov function in the parameterized function class, if exists, after collecting a finite number of counterexamples. We illustrate our method through numerical examples.
Cite
@article{arxiv.2110.00731,
title = {Learning Region of Attraction for Nonlinear Systems},
author = {Shaoru Chen and Mahyar Fazlyab and Manfred Morari and George J. Pappas and Victor M. Preciado},
journal= {arXiv preprint arXiv:2110.00731},
year = {2021}
}
Comments
Accepted to Conference on Decision and Control 2021