Learning Stability: AI-Driven Lyapunov Functions

Abstract

Lyapunov stability determines a system’s stability by constructing an energy-like function that decreases over time, thereby guaranteeing convergence to an equilibrium point without explicitly solving the nonlinear system equations. The main challenge lies in identifying an appropriate energy function. However, with recent advances in artificial intelligence, it has become possible to train AI models to learn and generate suitable Lyapunov functions based on the observed behavior of the system.