Optimal and minimum-energy optimal tracking of discrete linear time-varying systems

Based on the theory of generalized inverses and Bellman’s dynamic programming approach, two forms of solutions to the optimal and minimum-energy optimal tracking problems are presented for discrete linear time-varying systems. A further and detailed study on the optimal and minimum-energy optimal terminal control problem is given, where simple necessary and sufficient conditions for output controllability and reachability are obtained. As natural consequences, all the above solutions are reduced to give solutions to the optimal and minimum-energy optimal regulation problems. In each case, simple expressions for the minimum tracking error and minimum control energy are derived.