ABSTRACT
In this paper, optimal control problems for multi-stage and continuous-time linear singular systems are both considered. The singular systems are assumed to be regular and impulse-free. First, a recurrence equation is derived according to Bellman's principle of optimality in dynamic programming. Then, by applying the recurrence equation, bang-bang optimal controls for the control problems with linear objective functions subject to two types of multi-stage singular systems are obtained. Second, employing the principle of optimality, a equation of optimality for settling the optimal control problem subject to a class of continuous-time singular systems is proposed. The optimal control problem may become simpler through solving this equation of optimality. Two numerical examples and a dynamic input–output model are presented to show the effectiveness of the results obtained.
Acknowledgments
The authors would like to thank the Associate Editor and the reviewers for their constructive comments and suggestions, which have helped to improve the quality and clarity of this paper.
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No potential conflict of interest was reported by the authors.
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Notes on contributors
Yadong Shu
Yadong Shu is a PhD candidate in Department of Mathematics, Nanjing University of Science and Technology.
Yuanguo Zhu
Yuanguo Zhu is a professor of Mathematics in Nanjing University of Science and Technology located at No.200 Xiaolingwei Street, Nanjing 210094, Jiangsu, China. His research interests include uncertain systems, optimal control, optimization and intelligent computing.