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Optimal Control for Discrete‐time Descriptor Noncausal Systems

In this paper, optimal control problems governed by linear discrete‐time descriptor noncausal systems (with quadratic input variables) are investigated in order. A descriptor system assumed to be regular alone is called descriptor noncausal system. According to Bellman's principle of optimality in dynamic programming, a recurrence equation for simplifying the optimal control problems is derived. Then, employing the recurrence equation, a bang‐bang optimal control problem subject to a linear descriptor noncausal system and an optimal control problem subject to a descriptor noncausal system with quadratic input variables are both settled, and the optimal solutions are given through exact expressions. A numerical example is presented to illustrate the effectiveness of the results obtained concerning the bang‐bang optimal control problem.