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

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  • Yadong Shu
  • Yuanguo Zhu

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.

Suggested Citation

  • Yadong Shu & Yuanguo Zhu, 2018. "Optimal control for multi-stage and continuous-time linear singular systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(7), pages 1419-1434, May.
    • Handle: RePEc:taf:tsysxx:v:49:y:2018:i:7:p:1419-1434
    DOI: 10.1080/00207721.2018.1454534
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