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arXiv · 2605.09546

PolarNet: Single-Minima Neural Network for Modeling Lyapunov Functions

Yuan Zhong·Jiaxin Cheng·Hefu Ye·Yicong Zhou
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Abstract

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.

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BibTeXRIS

Yuan Zhong, Jiaxin Cheng, Hefu Ye, Yicong Zhou. 2026-05-10. PolarNet: Single-Minima Neural Network for Modeling Lyapunov Functions. https://arxiv.org/abs/2605.09546

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