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.
@article{arxiv.2505.03493,
title = {Sequentially learning regions of attraction from data},
author = {Oumayma Khattabi and Matteo Tacchi-Bénard and Sorin Olaru},
journal= {arXiv preprint arXiv:2505.03493},
year = {2025}
}