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

TL;DR

This paper introduces a data-driven approach to robust stabilization of nonlinear systems by optimizing Lyapunov functions to enlarge the domain of attraction, improving stability guarantees beyond existing methods.

Contribution

It proposes an optimization-based method to select Lyapunov functions that enlarge the robust domain of attraction for nonlinear control systems.

Findings

The method effectively enlarges the estimated domain of attraction.

Numerical results demonstrate improved stabilization performance.

The approach is applicable to non-affine nonlinear systems.

Abstract

Most of nonlinear robust control methods just consider the affine nonlinear nominal model. When the nominal model is assumed to be affine nonlinear, available information about existing non-affine nonlinearities is ignored. For non-affine nonlinear system, Li et al. (2019) proposes a new nonlinear control method to solve the robust stabilization problem with estimation of the robust closed-loop DOA (Domain of attraction). However, Li et al. (2019) assumes 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 by selecting an appropriate Lyapunov function. To achieve this goal, a solvable optimization problem is formulated to select an appropriate Lyapunov function from a parameterized positive-definite function set. The effectiveness of proposed method is verified by numerical results.