论文标题
神经Lyapunov控制具有稳定性的未知非线性系统
Neural Lyapunov Control of Unknown Nonlinear Systems with Stability Guarantees
论文作者
论文摘要
学习以正式保证的方式控制动态系统仍然是一项具有挑战性的任务。本文提出了一个学习框架，以同时使用神经控制器稳定未知的非线性系统，并学习神经Lyapunov功能，以证明闭环系统的吸引力区域（ROA）。算法结构由两个神经网络和一个满足模式理论（SMT）求解器组成。第一个神经网络负责学习未知的动态。第二个神经网络旨在确定有效的Lyapunov功能和可证明稳定的非线性控制器。然后，SMT求解器验证了候选Lyapunov功能确实满足Lyapunov条件。我们根据未知非线性系统的闭环稳定性提供了拟议的学习框架的理论保证。我们通过一组数值实验说明了该方法的有效性。
Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural Lyapunov function to certify a region of attraction (ROA) for the closed-loop system. The algorithmic structure consists of two neural networks and a satisfiability modulo theories (SMT) solver. The first neural network is responsible for learning the unknown dynamics. The second neural network aims to identify a valid Lyapunov function and a provably stabilizing nonlinear controller. The SMT solver then verifies that the candidate Lyapunov function indeed satisfies the Lyapunov conditions. We provide theoretical guarantees of the proposed learning framework in terms of the closed-loop stability for the unknown nonlinear system. We illustrate the effectiveness of the approach with a set of numerical experiments.
