Convex computation of regions of attraction from data using Sums-of-Squares programming

TL;DR

This paper introduces a data-driven method using Sum-of-Squares programming to compute outer approximations of the Region of Attraction for unknown dynamical systems, bypassing the need for explicit system models.

Contribution

It presents a novel approach that leverages data and the moment-SOS hierarchy to analyze RoA without requiring a polynomial system model.

Findings

Numerical experiments demonstrate effective RoA approximation from data.

The method shows potential for analyzing systems with limited model information.

Data quality influences the accuracy of the approximating sets.

Abstract

This paper focuses on the analysis of the Region of Attraction (RoA) for unknown autonomous dynamical systems. A data-driven approach based on the moment-Sum-of-Squares (SoS) hierarchy is proposed, enabling novel RoA outer approximations despite the reduced information on the dynamics. The main contribution consists of bypassing the system model and, hence, the recurring constraint on its polynomial structure. Numerical experiments showcase the influence of data on learned approximating sets, highlighting the potential of this method.