Efficient Construction of Neural Networks Lyapunov Functions with Domain Of Attraction Maximization

Benjamin Bocquillon (1, 2) , Philippe Feyel (2) , Guillaume Sandou (1) , Pedro Rodriguez-Ayerbe (1)

1 L2S - Laboratoire des signaux et systèmes
2 SAFRAN Electronics & Defense

This work deals with a new method for computing Lyapunov functions represented by neural networks for autonomous nonlinear systems. Based on the Lyapunov theory and the notion of domain of attraction, we propose an optimization method for determining a Lyapunov function modelled by a neural network while maximizing the domain of attraction. The potential of the proposed method is demonstrated by simulation examples.

Keywords: Lyapunov function; Domain of attraction; Optimization; Neural network; Nonlinear system

Domains: Engineering Sciences [physics]; Automatic

Benjamin Bocquillon, Philippe Feyel, Guillaume Sandou, Pedro Rodriguez-Ayerbe. Efficient Construction of Neural Networks Lyapunov Functions with Domain Of Attraction Maximization. 17th International Conference on Informatics in Control, Automation and Robotics (ICINCO), Jul 2020, Lieusaint, France. ⟨hal-02860869⟩