Learning Robust Control Lyapunov Functions through Lipschitz Neural Networks

Shiqing Wei; Prashanth Krishnamurthy; Farshad Khorrami

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arXiv · 2607.03713

Learning Robust Control Lyapunov Functions through Lipschitz Neural Networks

Shiqing Wei·Prashanth Krishnamurthy·Farshad Khorrami

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Abstract

This work presents a novel framework for learning robust control Lyapunov functions and stabilizing controllers for nonlinear dynamical systems subject to additive disturbances upper bounded by a state-dependent function. We leverage recent advances in Lipschitz neural networks to jointly learn both the Lyapunov functions and state-feedback controllers. We establish explicit bounds on the Hessian and third-order derivatives of these neural networks in the spectral norm, and introduce a GPU-friendly branch-and-bound algorithm that utilizes higher-order bounds to significantly accelerate the verification of the Lyapunov conditions. Finally, we validate the proposed approach through extensive simulations on six different dynamical systems.

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Shiqing Wei, Prashanth Krishnamurthy, Farshad Khorrami. 2026-07-04. Learning Robust Control Lyapunov Functions through Lipschitz Neural Networks. https://arxiv.org/abs/2607.03713

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