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Optimal Control for Discrete‐time Descriptor Noncausal Systems
Author(s) -
Shu Yadong
Publication year - 2021
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.2343
Subject(s) - optimal control , mathematics , control theory (sociology) , bang–bang control , quadratic equation , dynamic programming , control (management) , mathematical optimization , controller (irrigation) , computer science , artificial intelligence , geometry , agronomy , biology
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.