Estimation of Regions of Attraction with Formal Certificates in a Purely Data-Driven Setting

Alexandre Mauroy, Aivar Sootla

Abstract: We provide a Koopman operator based method to estimate the region of attraction of equilibria in a purely data-driven setting. The proposed method yields formal stability certificates, while not requiring prior knowledge of the system dynamics or online addition of data points along the way. It consists in three steps. First, a candidate Lyapunov is constructed through an approximated linear lifted dynamics. Next, the validity domain of the Lyapunov function is assessed from the data set. This validation step is performed with the sole knowledge of a (possibly loose) second-order bound on the flow, and without the usual a priori knowledge of a Lipschitz constant. Finally, an inner approximation of the region of attraction is obtained on an adaptive grid via a branch-and-bound algorithm.