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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.19398 |
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| _version_ | 1866916920558616576 |
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| author | Wang, Junkai Zhao, Yuxuan Zhou, Mi Zhang, Fumin |
| author_facet | Wang, Junkai Zhao, Yuxuan Zhou, Mi Zhang, Fumin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19398 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Robust Regions of Attraction Using Rollout-Enhanced Physics-Informed Neural Networks with Policy Iteration Wang, Junkai Zhao, Yuxuan Zhou, Mi Zhang, Fumin Systems and Control 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. |
| title | Learning Robust Regions of Attraction Using Rollout-Enhanced Physics-Informed Neural Networks with Policy Iteration |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2508.19398 |