Computation of Neural Networks Lyapunov Functions for Discrete and Continuous Time Systems with Domain of Attraction Maximization

Benjamin Bocquillon, Philippe Feyel, Guillaume Sandou, Pedro Rodriguez-Ayerbe

Abstract

This contribution deals with a new approach for computing Lyapunov functions represented by neural networks for nonlinear discrete-time systems to prove asymptotic stability. Based on the Lyapunov theory and the notion of domain of attraction, the proposed approach deals with an optimization method for determining a Lyapunov function modeled by a neural network while maximizing the domain of attraction. Several simulation examples are presented to illustrate the potential of the proposed method.

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