Optimal tracking for discrete-time systems with input delays

An optimal output tracking controller for discrete-time systems with input delay whose reference input to be tracked is an autonomous linear dynamic exosystem is addressed. Firstly, a method based on the so-called Artstein model reduction is extended to reduced the discrete-time system free of delay. Secondly, the optimal output tracking control (OOTC) problem without input delay is transformed into an equivalent optimal regulator problem by augmenting the state variables and then the optimal control input sequences are successfully derived by a so-called successive approximation approach (SAA). Finally, Simulations are presented to verify the effectiveness of the optimal tracking controller.