Journal of Guangdong University of Technology ›› 2018, Vol. 35 ›› Issue (01): 41-45,60.doi: 10.12052/gdutxb.170142

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Nash Differential Games for Delayed Nonlinear Stochastic Systems with State-and Control-dependent Noise

Li Jie-ming1, Zhu Huai-nian2   

  1. 1. School of International Education, Guangdong University of Technology, Guangzhou 511495, China;
    2. School of Economics & Commence, Guangdong University of Technology, Guangzhou 510520, China
  • Received:2017-09-27 Online:2018-01-09 Published:2017-12-22

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Abstract: The problem of two-person Nash differential games for delayed nonlinear stochastic systems with state- and control-dependent noise is discussed. A sufficient condition for the existence of the Nash equilibrium strategy is presented in terms of coupled Hamilton-Jacobi equations (HJEs). And meanwhile, the explicit expression of the equilibrium strategy is given. In the end, a numeric example is employed to show the effectiveness of the obtained results.

Key words: delayed nonlinear stochastic systems, differential game, Nash equilibrium, Hamilton-Jacobi equations

CLC Number: 

  • F224.32
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