Linear Model Predictive Control for Time Delay Systems

Abstract

<p>This paper studies linear model predictive control of real matrix-valued single delay systems. The delay system is written as an abstract inflnite-dimensional control system which is then mapped into an infinite-dimensional discrete-time control system using Cayley-Tustin discretization. A constrained model predictive control (MPC) problem is formulated for the discrete-time system where a terminal penalty function is utilized to cast the infinite-horizon optimization problem into a finite-horizon one. The proposed MPC design is demonstrated on an example of constrained stabilization of a 2 × 2 system. We will demonstrate that the proposed discrete-time MPC law not only stabilizes the discrete-time system but can be utilized in stabilizing the original continuoustime system as well, which is due to several favorable properties of the Cayley-Tustin discretization.</p>