The optimal control of delay discrete-time linear system with control constraint

The problem of optimal control of the delay discrete-time linear system with control constraint is considered, where the control input is the one-dimensional variable which takes its value in a bounded closed interval. By using dynamic programming, the problem of finding the optimal saturation control sequence that minimizes the performance index is transformed into that of finding the optimal saturation control sequence that minimizes the sequence of performance functional. The optimal saturation control sequence is derived by using the method of induction. Finally, the effectiveness of the proposed controller is shown by an example.