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The piecewise optimisation method for approximating uncertain optimal control problems under optimistic value criterion

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  • Bo Li
  • Yuanguo Zhu
  • Yuefen Chen

Abstract

In this paper, we introduce an approximate model and propose a piecewise optimisation method to simplify the expression of optimal control for an uncertain linear quadratic optimal control problem. First, we consider an optimal control problem of uncertain linear quadratic model under optimistic value criterion. Based on the equation of optimality, we deduce an analytic expression of optimal control. Then, we study an approximate model with control parameter and propose a piecewise optimisation method for solving the optimal parameter of such an approximate model. As an application, a four-wheel steering vehicle optimal control problem is given to show the utility of the proposed approximate model and the efficiency of the proposed piecewise optimisation method.

Suggested Citation

  • Bo Li & Yuanguo Zhu & Yuefen Chen, 2017. "The piecewise optimisation method for approximating uncertain optimal control problems under optimistic value criterion," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(8), pages 1766-1774, June.
    • Handle: RePEc:taf:tsysxx:v:48:y:2017:i:8:p:1766-1774
    DOI: 10.1080/00207721.2017.1282061
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    Cited by:

    1. Wang, Xiao & Ning, Yufu & Peng, Zhen, 2020. "Some results about uncertain differential equations with time-dependent delay," Applied Mathematics and Computation, Elsevier, vol. 366(C).
    2. Li, Bo & Zhang, Ranran & Jin, Ting & Shu, Yadong, 2021. "Parametric approximate optimal control of uncertain differential game with application to counter terror," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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