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arXiv · 2508.19398

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

Junkai Wang·Yuxuan Zhao·Mi Zhou·Fumin Zhang
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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.

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Junkai Wang, Yuxuan Zhao, Mi Zhou, Fumin Zhang. 2025-08-26. Learning Robust Regions of Attraction Using Rollout-Enhanced Physics-Informed Neural Networks with Policy Iteration. https://arxiv.org/abs/2508.19398

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