An Approach to Mismatched Disturbance Rejection Control for Uncontrollable Systems

TL;DR

This paper presents a novel linear quadratic tracking approach for mismatched disturbance rejection in uncontrollable linear discrete-time systems, providing conditions for solvability and stabilization, with demonstrated effectiveness through examples.

Contribution

Introduces a new quadratic performance index transforming disturbance rejection into a linear quadratic tracking problem for uncontrollable systems.

Findings

Derived necessary and sufficient conditions for finite horizon solvability.

Established sufficient conditions for infinite horizon stabilization.

Validated the approach with four illustrative examples.

Abstract

This study focuses on the problem of optimal mismatched disturbance rejection control for uncontrollable linear discrete-time systems. In contrast to previous studies, by introducing a quadratic performance index such that the regulated state can track a reference trajectory and minimize the effects of disturbances, mismatched disturbance rejection control is transformed into a linear quadratic tracking problem. The necessary and sufficient conditions for the solvability of this problem over a finite horizon and a disturbance rejection controller are derived by solving a forward-backward difference equation. In the case of an infinite horizon, a sufficient condition for the stabilization of the system is obtained under the detectable condition. This paper details our novel approach to disturbance rejection. Four examples are provided to demonstrate the effectiveness of the proposed method.