Dead-beat model predictive control for discrete-time linear systems

TL;DR

This paper introduces a dead-beat model predictive control approach for discrete-time linear systems, ensuring deadbeat performance with theoretical guarantees for both constrained and unconstrained cases.

Contribution

It develops a novel MPC framework that guarantees deadbeat control in discrete-time linear systems, including constraints, with proven recursive feasibility and performance.

Findings

Unconstrained deadbeat MPC achieved by setting control horizon to system dimension.

Constrained deadbeat MPC designed with terminal cost penalty, ensuring feasibility.

Theoretical proofs confirm deadbeat performance and recursive feasibility.

Abstract

In this paper, model predictive control (MPC) strategies are proposed for dead-beat control of linear systems with and without state and control constraints. In unconstrained MPC, deadbeat performance can be guaranteed by setting the control horizon to the system dimension, and adding an terminal equality constraint. It is proved that the unconstrained deadbeat MPC is equivalent to linear deadbeat control. The proposed constrained deadbeat MPC is designed by setting the control horizon equal to the system dimension and penalizing only the terminal cost. The recursive feasibility and deadbeat performance are proved theoretically.