Sequentially learning regions of attraction from data

TL;DR

This paper presents a data-driven method to iteratively learn and refine the region of attraction for unknown dynamical systems using piecewise affine Lyapunov functions and domain tessellation.

Contribution

It introduces an optimization-based iterative approach to certify and improve the estimate of the basin of attraction for unknown systems.

Findings

Effective certification of the domain of attraction.

Iterative refinement improves the Lyapunov function accuracy.

Method applicable with point-wise system evaluations.

Abstract

The paper is dedicated to data-driven analysis of dynamical systems. It deals with certifying the basin of attraction of a stable equilibrium for an unknown dynamical system. It is supposed that point-wise evaluation of the right-hand side of the ordinary differential equation governing the system is available for a set of points in the state space. Technically, a Piecewise Affine Lyapunov function will be constructed iteratively using an optimisation-based technique for the effective validation of the certificates. As a main contribution, whenever those certificates are violated locally, a refinement of the domain and the associated tessellation is produced, thus leading to an improvement in the description of the domain of attraction.