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Optimal control for uncertain random singular systems with multiple time-delays

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  • Chen, Xin
  • Zhu, Yuanguo

Abstract

Chance theory provides us a useful tool to solve an optimal control problem with indeterminacy composing of both uncertainty and randomness. Based on chance theory, this paper studies an optimal control for uncertain random singular systems with multiple time-delays. First, an uncertain random singular system with multiple time-delays is introduced, and then the corresponding optimal control problem is established. The equivalent relationship between this problem and the optimal control problem for standard uncertain random systems is derived. Then the appropriate recurrence equations are proposed according to the dynamic programming method. Furthermore, two kinds of optimal control problems are discussed. The optimal control inputs and respective optimal values of the problems are provided via the solvability of the obtained equations. Finally, a numerical example is presented to show the effectiveness of our theoretical results.

Suggested Citation

  • Chen, Xin & Zhu, Yuanguo, 2021. "Optimal control for uncertain random singular systems with multiple time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    • Handle: RePEc:eee:chsofr:v:152:y:2021:i:c:s0960077921007256
    DOI: 10.1016/j.chaos.2021.111371
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    References listed on IDEAS

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    1. Li, Bo & Zhang, Ranran, 2021. "A new mean-variance-entropy model for uncertain portfolio optimization with liquidity and diversification," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    2. Meilin Wen & Rui Kang, 2016. "Reliability analysis in uncertain random system," Fuzzy Optimization and Decision Making, Springer, vol. 15(4), pages 491-506, December.
    3. Luenberger, David G & Arbel, Ami, 1977. "Singular Dynamic Leontief Systems," Econometrica, Econometric Society, vol. 45(4), pages 991-995, May.
    4. Qin, Zhongfeng, 2015. "Mean-variance model for portfolio optimization problem in the simultaneous presence of random and uncertain returns," European Journal of Operational Research, Elsevier, vol. 245(2), pages 480-488.
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    Cited by:

    1. Shen, Jiayu & Shi, Jianxin & Gao, Lingceng & Zhang, Qiang & Zhu, Kai, 2023. "Uncertain green product supply chain with government intervention," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 136-156.
    2. Jia, Zhifu & Liu, Xinsheng, 2023. "Uncertain stochastic hybrid differential game system with V-n jumps: Saddle point equilibrium strategies and application to advertising duopoly game," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Nosrati, Komeil & Belikov, Juri & Tepljakov, Aleksei & Petlenkov, Eduard, 2023. "Extended fractional singular kalman filter," Applied Mathematics and Computation, Elsevier, vol. 448(C).
    4. Xu, Qinqin & Zhu, Yuanguo, 2022. "Reliability modeling of uncertain random fractional differential systems with competitive failures," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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