Local Asymptotic Stability Analysis and Region of Attraction Estimation with Gaussian Processes

Abstract

Determining the region of attraction of nonlinear systems is a difficult problem, which is typically approached by means of Lyapunov theory. State of the art approaches either provide high flexibility regarding the Lyapunov function or parallelizability of computation. Aiming at both, flexibility and parallelizability, we propose a method to obtain a Lyapunov-like function for stability analysis by learning the infinite horizon cost function with a Gaussian process based on approximate dynamic programming. We develop a novel approach to char-acterize the region of attraction using a Lyapunov-like function, which is analyzed with a sampling-based interval analysis algorithm. Since each interval can be examined independently, the algorithm allows both parallelizable analysis and flexible construction of the Lyapunov-like function.