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
李洁茗(1985–),女,助教,硕士,主要研究方向为博弈论及商务管理
网络首发:2018-01-09,
纸质出版:2018
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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.
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.
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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