Feedback Stabilization and Output Tracking for Discrete-Time Lipschitz Nonlinear Systems via Iterative Convex Approximations

TL;DR

This paper presents a new iterative convex approximation method for designing full-state feedback controllers for discrete-time Lipschitz nonlinear systems, enhancing stabilization and output tracking performance.

Contribution

It introduces a simple iterative approach for full-state feedback control and extends it to output tracking, addressing a less developed area in nonlinear control design.

Findings

Effective stabilization of Lipschitz nonlinear systems achieved.

Method improves convergence of closed-loop performance.

Extension to output tracking demonstrated successfully.

Abstract

The stabilization of unstable nonlinear systems and tracking control are challenging engineering problems due to the encompassed nonlinearities in dynamic systems and their scale. In the past decades, numerous observer-based control designs for dynamic systems in which the nonlinearity belongs to Lipschitz functions have been proposed. However, most of them only focus on output feedback and consequently, state feedback design remains less developed. To that end, this paper is dedicated to the problem of full-state feedback controller design for discrete-time Lipschitz nonlinear systems. In addition, we present a simple iterative method for improving the convergence of the closed-loop performance. It is later demonstrated that our approach can be conveniently extended and utilized for output tracking.