Nash Differential Games of Singular Stochastic Affine Systems with Multiple Decision Makers

Li Jie-ming; Zhu Huai-nian; Zhang Cheng-ke

doi:10.3969/j.issn.1007-7162.2016.04.007

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Nash Differential Games of Singular Stochastic Affine Systems with Multiple Decision Makers

更新时间：2026-05-27

- Nash Differential Games of Singular Stochastic Affine Systems with Multiple Decision Makers
- Vol. 33, Issue 4, Pages: 37-43(2016)
- 作者机构：
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- DOI：10.3969/j.issn.1007-7162.2016.04.007
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- Published：2016
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李洁茗, 朱怀念, 张成科. 广义随机系统的多人Nash微分博弈[J]. 广东工业大学学报, 2016, 33(4): 37-43.

Li Jie-ming, Zhu Huai-nian, Zhang Cheng-ke. Nash Differential Games of Singular Stochastic Affine Systems with Multiple Decision Makers[J]. 2016, 33(4): 37-43.
李洁茗, 朱怀念, 张成科. 广义随机系统的多人Nash微分博弈[J]. 广东工业大学学报, 2016, 33(4): 37-43. DOI： 10.3969/j.issn.1007-7162.2016.04.007.

Li Jie-ming, Zhu Huai-nian, Zhang Cheng-ke. Nash Differential Games of Singular Stochastic Affine Systems with Multiple Decision Makers[J]. 2016, 33(4): 37-43. DOI： 10.3969/j.issn.1007-7162.2016.04.007.

摘要

研究了一类连续时间广义随机系统的多人Nash微分博弈问题.在定义了广义随机系统稳定性的相关概念后，通过一个线性矩阵不等式(linear matrix inequality

LMI)首先给出了系统稳定性的条件.然后，研究了有限时间和无限时间的广义随机系统的多人Nash微分博弈，利用Riccati方程法得到了均衡策略的存在条件等价于耦合的微分或代数Riccati方程存在解，并给出了均衡策略的显式表达及最优性能指标值.最后，将所得的结果应用于现代鲁棒控制中的随机H

∞

控制问题，得到了鲁棒控制策略的存在条件及显式表达.

Abstract

A class of Nash differential games of continuoustime singular stochastic affine systems with multiple decision makers is investigated. After establishing some concepts of the stability for stochastic singular systems

the condition of the stability is presented by means of a linear matrix inequality. Then

by utilizing Riccati equation approach

the existence conditions of equilibrium strategy set in finite horizon and infinite horizon are obtained by means of a set of cross coupled differential Riccati equations or a set of cross coupled algebraic Riccati equations

respectively. And explicit expressions of the optimal feedback controls and optimal cost function are given. In the end

the obtained results are used to deal with the stochastic H

∞

control problem in the fields of mod

ern robust control theory

and the existence conditions of robust control strategies and explicit expressions are obtained.

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