ABSTRACT
This chapter presents the optimal control of discrete-time systems. It discusses the state regulator system, and provides closed-loop optimal control configuration for discrete-time systems. This leads us to matrix difference Riccati equation. The solution of the matrix difference Riccati equation is critical for linear quadratic regulator system. The chapter addresses linear quadratic tracking problem for a discrete-time system and are interested in obtaining a closed-loop control scheme that enables a given system track a desired trajectory over the given interval of time. It deals with linear, time-invariant systems in order to get some elegant results although the method can as well be applied to nonlinear, time-varying case. The chapter explores the frequency domain to derive some results from the classical control point of view for a linear, time-invariant, discrete-time, optimal control system with infinite-time case.
