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Linear Quadratic Nash Differential Games of Stochastic Singular Systems

Author

Listed:
  • Zhou Haiying

    (School of Management, Guangdong University of Technology, Guangzhou510520, China)

  • Zhu Huainian

    (School of Management, Guangdong University of Technology, Guangzhou510520, China)

  • Zhang Chengke

    (School of Economics and Commerce, Guangdong University of Technology, Guangzhou510520, China)

Abstract

In this paper, we deal with the Nash differential games of stochastic singular systems governed by Itô-type equation in finite-time horizon and infinite-time horizon, respectively. Firstly, the Nash differential game problem of stochastic singular systems in finite time horizon is formulated. By applying the results of stochastic optimal control problem, the existence condition of the Nash strategy is presented by means of a set of cross-coupled Riccati differential equations. Similarly, under the assumption of the admissibility of the stochastic singular systems, the existence condition of the Nash strategy in infinite-time horizon is presented by means of a set of cross-coupled Riccati algebraic equations. The results show that the strategies of each players interact.

Suggested Citation

  • Zhou Haiying & Zhu Huainian & Zhang Chengke, 2014. "Linear Quadratic Nash Differential Games of Stochastic Singular Systems," Journal of Systems Science and Information, De Gruyter, vol. 2(6), pages 553-560, December.
    • Handle: RePEc:bpj:jossai:v:2:y:2014:i:6:p:553-560:n:6
    DOI: 10.1515/JSSI-2014-0553
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    References listed on IDEAS

    as
    1. E. K. Boukas, 2008. "On State Feedback Stabilization of Singular Systems with Random Abrupt Changes," Journal of Optimization Theory and Applications, Springer, vol. 137(2), pages 335-345, May.
    2. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, September.
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