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

Li Jie-ming; Zhu Huai-nian

doi:10.12052/gdutxb.170142

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

更新时间：2026-05-27

- Nash Differential Games for Delayed Nonlinear Stochastic Systems with State-and Control-dependent Noise
- Vol. 35, Issue 1, Pages: 41-45(2018)
- 作者机构：
  
  1. 广东工业大学　国际教育学院,广东,广州,511495
  2. 广东工业大学　经济与贸易学院,广东,广州,510520
- 作者简介：
- 基金信息：
- DOI：10.12052/gdutxb.170142
  CLC： F224.32
- Online First：09 January 2018，
  
  Published：2018
- 稿件说明：
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李洁茗, 朱怀念. 噪声依赖状态和控制的时滞非线性随机系统Nash微分博弈[J]. 广东工业大学学报, 2018, 35(1): 41-45.

Li Jie-ming, Zhu Huai-nian. Nash Differential Games for Delayed Nonlinear Stochastic Systems with State-and Control-dependent Noise[J]. 2018, 35(1): 41-45.
李洁茗, 朱怀念. 噪声依赖状态和控制的时滞非线性随机系统Nash微分博弈[J]. 广东工业大学学报, 2018, 35(1): 41-45. DOI： 10.12052/gdutxb.170142.

Li Jie-ming, Zhu Huai-nian. Nash Differential Games for Delayed Nonlinear Stochastic Systems with State-and Control-dependent Noise[J]. 2018, 35(1): 41-45. DOI： 10.12052/gdutxb.170142.

摘要

研究了一类噪声依赖于状态和控制的时滞非线性随机系统的2人Nash微分博弈问题

借助4个耦合的Hamilton-Jacobi方程组(HJEs)得到了Nash均衡策略存在的充分条件

即耦合HJEs如果存在解

Nash均衡策略就存在. 同时给出了Nash均衡策略的显式表达. 最后

通过一个数值算例验证了文中所得结论的有效性.

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.

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Keywords

references

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