Interval-driven discrete-time general nonlinear robust control: stabilization with closed-loop robust DOA enlargement

TL;DR

This paper introduces an interval analysis-based numerical method to design unstructured robust controllers for discrete-time nonlinear systems, significantly enlarging the domain of attraction without relying on Lyapunov level-sets.

Contribution

It proposes a novel interval analysis approach to estimate unstructured robust controllers, removing Lyapunov level-set constraints and enlarging the robust domain of attraction.

Findings

Enlarged robust domain of attraction compared to existing methods

Validated approach through simulation demonstrating improved RDOA

Removed limitations of Lyapunov level-set constraints

Abstract

This paper presents new results that allow one to address the discrete-time general nonlinear robust control problem. The uncertain system is described by a general nonlinear function set characterized by the nominal model and the corresponding modeling error bound. Traditional synthesis methods design parameters of a structured robust controller. The key aim of this paper is to find an unstructured robust controller set in the state-control space, which enlarges the estimate of the closed-loop robust domain of attraction (RDOA). Based on the interval analysis arithmetic, a numerical method to estimate the unstructured robust controller set is proposed and the rigorous convergence analysis is given. The existing RDOA results are constrained by the level-set of the Lyapunov function, whereas the results in this paper remove this limitation. Furthermore, a solvable optimization problem is formulated so the estimate of RDOA is enlarged by selecting a Lyapunov function from a Lyapunov function set of sum-of-squares polynomials. The method is then validated by a specific case simulation study and results show more extensive RDOA than the previous methods.