通过李普希茨神经网络学习鲁棒控制李雅普诺夫函数
Learning Robust Control Lyapunov Functions through Lipschitz Neural Networks
- New York University（纽约大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出学习鲁棒控制李雅普诺夫函数和稳定控制器的新框架，利用李普希茨神经网络联合学习，建立神经网络高阶导数边界并引入算法加速验证，通过模拟验证方法。
AI中文摘要：
本文提出了一种新框架，用于学习受状态依赖函数上界约束的加性干扰的非线性动力系统的鲁棒控制李雅普诺夫函数和稳定控制器。我们利用李普希茨神经网络的最新进展来联合学习李雅普诺夫函数和状态反馈控制器。我们在谱范数中建立了这些神经网络的海森矩阵和三阶导数的显式边界，并引入了一种GPU友好的分支定界算法，该算法利用高阶边界来显著加速李雅普诺夫条件的验证。最后，我们通过对六个不同动力系统的广泛模拟来验证所提出的方法。
英文摘要：
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.
