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Parametric approximate optimal control of uncertain differential game with application to counter terror

Author

Listed:
  • Li, Bo
  • Zhang, Ranran
  • Jin, Ting
  • Shu, Yadong

Abstract

The linear quadratic differential game plays an important role in many fields. It is well known that the saddle point of linear quadratic differential game is given in a feedback form with a solution of Riccati differential equation. However, the control-related Riccati differential equation cannot be solved analytically in many cases. Then the optimal controls may be difficult to be implemented in practice. In order to simplify the forms of optimal controls, in this paper, we investigate a parametric approximate optimal control problem of linear quadratic differential game under uncertain environment. First, we introduce an uncertain linear quadratic differential game model and its analytic optimal controls. Then, an uncertain linear quadratic differential game model with constrained parametric control domain is formulated. Moreover, a parametric approximate optimization method is presented for solving the optimal control parameters. Finally, a counter terror problem is analyzed to show the efficiency of our presented method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002940
    DOI: 10.1016/j.chaos.2021.110940
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    References listed on IDEAS

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    1. Jin, Ting & Zhu, Yuanguo, 2020. "First hitting time about solution for an uncertain fractional differential equation and application to an uncertain risk index model," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    2. 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.
    3. A. J. Novak & G. Feichtinger & G. Leitmann, 2010. "A Differential Game Related to Terrorism: Nash and Stackelberg Strategies," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 533-555, March.
    4. G. Feichtinger & A. J. Novak, 2008. "Terror and Counterterror Operations: Differential Game with Cyclical Nash Solution," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 541-556, December.
    5. Feichtinger, Gustav & Jorgensen, Steffen, 1983. "Differential game models in management science," European Journal of Operational Research, Elsevier, vol. 14(2), pages 137-155, October.
    6. Yang, Xiangfeng & Liu, Yuhan & Park, Gyei-Kark, 2020. "Parameter estimation of uncertain differential equation with application to financial market," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    7. Xiangfeng Yang & Kai Yao, 2017. "Uncertain partial differential equation with application to heat conduction," Fuzzy Optimization and Decision Making, Springer, vol. 16(3), pages 379-403, September.
    8. I. N. Katz & H. Mukai & H. Schättler & M. Zhang & M. Xu, 2005. "Solution of a Differential Game Formulation of Military Air Operations by the Method of Characteristics," Journal of Optimization Theory and Applications, Springer, vol. 125(1), pages 113-135, April.
    9. Yun Sun & Yuanguo Zhu, 2017. "Bang–bang property for an uncertain saddle point problem," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 605-613, March.
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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. Xiang Wang & Chang-Franw Lee & Jiabei Jiang & Xiaoyang Zhu, 2023. "Discussion on Sustainable Development Strategy of China’s Rehabilitation Assistive Device Industry Based on Diamond Model," Sustainability, MDPI, vol. 15(3), pages 1-24, January.
    3. Li, Bo & Huang, Tian, 2022. "Control variable parameterization and optimization method for stochastic linear quadratic models," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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