Optimal control for multi-stage and continuous-time linear singular systems

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.

KEYWORDS:

• Linear singular systems
• optimal control
• Bellman's principle of optimality
• equation of optimality

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.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [grant number 61673011]; Postgraduate Research & Practice Innovation Program of Jiangsu Province [grant number KYCX17_0318].

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.