Design of an optimal preview controller for linear time-varying discrete systems in a multirate setting

Abstract

This paper is concerned with preview control problems for linear time-varying discrete systems in a multirate setting. First, by using the discrete lifting technique, the multirate time-varying discrete system is converted to a formal single-rate system. Then, by applying the standard linear quadratic (LQ) preview control method, we construct the expanded error system, and the optimal preview control model of the common time-varying discrete system is obtained. The optimal control input of the expanded error system is obtained by using the outcome of optimal control theory on time-varying systems. The controller with preview action is obtained when we transfer our conclusion into the original system. Finally, a numerical example is included to illustrate the validity of the proposed method.