Locally Convex Neural Lyapunov Functions and Region of Attraction Maximization for Stability of Nonlinear Systems

Lucas Hugo, Philippe Feyel, David Saussié

2023

Abstract

The Lyapunov principle involves to find a positive Lyapunov function with a local minimum at the equilibrium point, whose time derivative is negative with a local maximum at that point. As a validation, it is usual to check the sign of the Hessian eigenvalues which can be complex: it requires to know a formal expression of the system dynamics, and especially a differentiable one. In order to circumvent this, we propose in this paper a scheme allowing to validate these functions without computing the Hessian. Two methods are proposed to force the convexity of the function near the equilibrium; one uses a neural single network to model the Lyapunov function, the other uses an additional one to approximate its time derivative. The training process is designed to maximize the region of attraction of the locally convex neural Lyapunov function trained. The use of examples allows us to validate the efficiency of this approach, by comparing it with the Hessian-based approach.

Paper Citation

in Harvard Style

Hugo L., Feyel P. and Saussié D. (2023). Locally Convex Neural Lyapunov Functions and Region of Attraction Maximization for Stability of Nonlinear Systems. In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO; ISBN 978-989-758-670-5, SciTePress, pages 29-36. DOI: 10.5220/0012180300003543

in Bibtex Style

@conference{icinco23,
author={Lucas Hugo and Philippe Feyel and David Saussié},
title={Locally Convex Neural Lyapunov Functions and Region of Attraction Maximization for Stability of Nonlinear Systems},
booktitle={Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO},
year={2023},
pages={29-36},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012180300003543},
isbn={978-989-758-670-5},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO
TI - Locally Convex Neural Lyapunov Functions and Region of Attraction Maximization for Stability of Nonlinear Systems
SN - 978-989-758-670-5
AU - Hugo L.
AU - Feyel P.
AU - Saussié D.
PY - 2023
SP - 29
EP - 36
DO - 10.5220/0012180300003543
PB - SciTePress