Data-Driven Robust Stabilization with Robust DOA Enlargement for Nonlinear Systems

Abstract

This paper present a method based on simulation data to optimize Lyapunov functions to stabilize nonlinear systems such that an estimation of the domain of attraction (DOA) is maximized. For non-affine nonlinear system, our previous work proposes an approach to estimate robust closed-loop DOA for uncertain nonlinear systems by sampling the state- and input-space. However, the main drawback is that the Lyapunov function is given and does not consider the problem of finding a good Lyapunov function to enlarge the estimate of the robust closed-loop DOA. The motivation of this paper is to enlarge the estimate of the closed-loop DOA in order to reduce conservatism of the DOA estimate. To achieve this goal, a solvable optimization problem is formulated to use sum-of-squares techniques to evaluate the cost for a given Lyapunov function and then optimizing over Lyapunov functions via existing meta-heuristic optimization methods. The effectiveness of proposed method is verified by numerical results.