Empirical approximation for Lyapunov functions with artificial neural nets

Abstract

An artificial neural network is proposed as a function approximator for empirical modeling of a Lyapunov function for a nonlinear dynamic system that projects stable behavior as potentially observable in its state space. The theoretical framework for the methodology of designing the so-called Lyapunov neural network, which empirically models a Lyapunov function, is described. Algorithms for training the Lyapunov neural network for a neurodynamics system are presented.