Deep Lyapunov Function: Automatic Stability Analysis for Dynamical Systems

Abstract: Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which is mainly studied by Lyapunov's stability theory. This theory requires finding a function with specified properties. Except for a few simple examples, there is no straightforward constructive algorithm to find a Lyapunov function for an arbitrary dynamical system. The goal of this work is proposing a simple yet effective way to approximate this function using deep learning tools.