PolarNet: Single-Minima Neural Network for Modeling Lyapunov Functions
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910207127322624 |
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| author | Zhong, Yuan Cheng, Jiaxin Ye, Hefu Zhou, Yicong |
| author_facet | Zhong, Yuan Cheng, Jiaxin Ye, Hefu Zhou, Yicong |
| contents | Learning control strategies with provable stability guarantees continues to be a challenging problem. In this work, we examine a family of training-time behaviors exhibited by existing neural Lyapunov control methods under specific conditions, which can hinder the synthesis of a provably stable controller. We identify the root cause as the lack of neural network architectural guarantees on the learned Lyapunov function, and propose PolarNet, a network architecture that provably addresses these issues by structurally guarantee to have a single critical point. We provide theoretical guarantee regarding the properness and universality of PolarNet for modeling Lyapunov functions, and show that using it as a drop-in replacement in existing neural Lyapunov control methods can effectively circumvent particular difficulties in training. We conduct a set of numerical experiments to verify that PolarNet consistently maintains a single critical point and, when used as a drop-in replacement in existing neural Lyapunov control methods, successfully avoids training failures caused by the lack of architectural guarantees. The code of this paper is available at https://github.com/23-zy/PolarNet. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09546 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | PolarNet: Single-Minima Neural Network for Modeling Lyapunov Functions Zhong, Yuan Cheng, Jiaxin Ye, Hefu Zhou, Yicong Systems and Control Learning control strategies with provable stability guarantees continues to be a challenging problem. In this work, we examine a family of training-time behaviors exhibited by existing neural Lyapunov control methods under specific conditions, which can hinder the synthesis of a provably stable controller. We identify the root cause as the lack of neural network architectural guarantees on the learned Lyapunov function, and propose PolarNet, a network architecture that provably addresses these issues by structurally guarantee to have a single critical point. We provide theoretical guarantee regarding the properness and universality of PolarNet for modeling Lyapunov functions, and show that using it as a drop-in replacement in existing neural Lyapunov control methods can effectively circumvent particular difficulties in training. We conduct a set of numerical experiments to verify that PolarNet consistently maintains a single critical point and, when used as a drop-in replacement in existing neural Lyapunov control methods, successfully avoids training failures caused by the lack of architectural guarantees. The code of this paper is available at https://github.com/23-zy/PolarNet. |
| title | PolarNet: Single-Minima Neural Network for Modeling Lyapunov Functions |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2605.09546 |