Optimal Control for Discrete‐time Descriptor Noncausal Systems
Yadong Shu
Abstract
Abstract 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.