Learning Robust Regions of Attraction Using Rollout-Enhanced Physics-Informed Neural Networks with Policy Iteration

TL;DR

This paper introduces a neural network-based method using policy iteration and rollout to accurately compute the robust region of attraction for perturbed systems by solving the generalized Zubov's equation.

Contribution

It presents a novel physics-informed neural network framework with policy iteration and rollout to solve the nonlinear generalized Zubov's equation for robustness analysis.

Findings

Effective approximation of the viscosity solution demonstrated in simulations.

The method handles high-dimensional systems successfully.

Neural network-generated value estimates improve training stability.

Abstract

The region of attraction is a key metric of the robustness of systems. This paper addresses the numerical solution of the generalized Zubov's equation, which produces a special Lyapunov function characterizing the robust region of attraction for perturbed systems. To handle the highly nonlinear characteristic of the generalized Zubov's equation, we propose a physics-informed neural network framework that employs a policy iteration training scheme with rollout to approximate the viscosity solution. In addition to computing the optimal disturbance during the policy improvement process, we incorporate neural network-generated value estimates as anchor points to facilitate the training procedure to prevent singularities in both low- and high-dimensional systems. Numerical simulations validate the effectiveness of the proposed approach.