Optimum Sampled-Data Control System Design by Dynamic Programming Technique

Abstract

In this paper, the authors deal with an application of dynamic programming technique to an optimum sampled-data control system design. Since the optimum sampled-data control problem may be treated as an n-stage decision process, the determination of the optimum control law is carried out by means of the dynamic programming technique. Optimum control policies are derived to fulfill the minimum integral squared error for the deterministic case and the minimum expected value of integral squared error for the stochastic case. It is shown that the control signal of the optimum system consists of a linear combination of system variables. The over-all optimum control system is a time-varying system. However, the quasi-optimum control can be achieved by feeding back all the state variables through appropriate constant multipliers and the quasi-optimum control system can be considered as a good approximation of the optimum system.