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

Abstract: The paper concentrates on the analysis of the region of attraction (ROA) for unknown autonomous dynamical systems. The aim is to explore a data-driven approach based on moment-sum-of-squares (SoS) hierarchy, which enables novel RoA outer approximations despite the reduced information on the structure of the dynamics. The main contribution of this work is bypassing the system model and, consequently, the recurring constraint on its polynomial structure. Numerical experimentation showcases the influence of data on learned approximating sets, offering a promising outlook on the potential of this method.