Approximate Design To Optimal Output Tracking Controllers For Discrete-time Systems With Time-delay

Time-delay is quite common in practical control systems. The optimal control problems of time-delay systems are always the important aspects of scientific research. With the development of computer science, the control problem of discrete systems also becomes a focus of attention. Digital controller replaced analog controller in most cases. Based on the need of the practical engineering, the control problem of discrete system has quite a lot practical applications. So the optimal control problem of discrete-time systems with time-delay becomes a wildly attentional research field in recent decades. But there are some difficulties in respectively research of discrete-time systems. On the one hand, although discrete time-delay systems can be studied by expanding its dimensions and then being translated into systems without time-delay, the systems with high dimension and/or long time-delay will fall into "dimension disaster", which will cause order increase of the systems model and bring on computing complexity increase at geometric progression. On the other hand, the optimal control problem for time-delay systems with quadratic performance index always leads to a two-point boundary value problem with both delay and advance terms, which is very difficult to be solved precisely. So solving the suboptimal control law is one of the important aims of researchers. As a research field of control theory, the theory of tracking control has been wildly applied in practical engineering. For the optimal output tracking control (OOTC) problem of discrete-time systems with time-delay, quite attentions have been taken in recent years.This paper is concerned with the optimal output tracking control for time-delay discrete-time systems with quadratic performance index. Firstly this paper reviews the characteristics of time-delay discrete-time systems and main results of related research field; and then summarizes the development of optimal control theory and its important application-tracking control; finally introduce the sensitivity approach into the study of the OOTC problem of time-delay discrete-time systems and discuss the solution and reality of the OOTC law in detail.By introducing a sensitivity parameter, the original optimal output tracking control problem is transformed into a series of two-point boundary value problems without delay or advance terms. Then by solving the two-point boundary value problem sequence recursively, the optimal output tracking control law consisting of linear analytic functions and a compensation term is obtained. The analytic functions can be solved by a Riccati equation and matrix equation. The compensation term can be obtained by a recursion formula of adjoint vector equations.In this paper, first for finite-time and infinite-time performance index, the solving process of the problems have been expounded and demonstrated respectively. Then the physically realizable problem of the optimal control law has been discussed. Finally, simulation examples are employed to test the validity of the presented sensitivity algorithm.In the end of this paper, the main works of this paper have been concluded and the sensitivity approach for discrete large-scale systems with time-delay has been analyzed briefly.