Expected value based optimal control for discrete-time stochastic noncausal systems

In this paper, optimal control models subject to two types of discrete-time stochastic noncausal systems are considered in order. The stochastic noncausal systems are stochastic singular systems assumed to be regular alone. Based on the principle of dynamic programming, a recurrence equation is deduced to simplify the optimal control models. Then, by applying the recurrence equation, a bang-bang optimal control problem ruled by a linear stochastic noncausal system and an optimal control problem for a stochastic noncausal system with quadratic inputs are both solved, and the optimal solutions are presented through analytical expressions. A numerical example is provided to illustrate the effectiveness of the results about the bang-bang optimal control problem.