奇异随机Markov跳变系统的N人Nash博弈问题

曹铭, 朱怀念, 张成科, 程硕

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (3) : 700-712.

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PDF(406 KB)
系统科学与数学 ›› 2017, Vol. 37 ›› Issue (3) : 700-712. DOI: 10.12341/jssms13096
论文

奇异随机Markov跳变系统的N人Nash博弈问题

    曹铭1,朱怀念2,张成科2,程硕3
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Nash Games of Singular Stochastic Markov Jump Systems with \bmN Decision Makers

    CAO Ming1 ,ZHU Huainian2 ,ZHANG Chengke2 ,CHENG Shuo3
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摘要

分别研究了有限时间和无限时间情形下的一类奇异随机Markov跳变系统的N人微分博弈问题.利用配方 法, 得到了有限时间N人博弈的Nash均衡策略的微分Riccati 方程, 证明了Nash均衡策略的存在条件等价于微分Riccati 方程存在解;无限时间内, N人博弈的Nash均衡策略的存在条件 等价于代数Riccati方程存在解, 并分别给出了均衡策略的显式表达及最优性能泛函值.最后, 将所得的结果应用于现代鲁棒控制中的随机Missing dimension or its units for \kern 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 Markov jump systems of with multiple decision makers is investigated in this paper. Both the cases of finite-time horizon and infinite-time horizon are discussed, respectively. By utilizing the square completion technique, the existence conditions of Nash equilibrium is obtained by differential Riccati equations in finite-time horizon, and the existence conditions of Nash equilibrium is obtained by algebra Riccati equations in infinite-time horizon. Explicit expressions of equilibrium strategy and optimal performance functional are given. In the end, we use the obtained results to deal with the stochastic Missing dimension or its units for \kern control problem in the fields of modern robust control, and the existence condition of robust control strategies and explicit expression are obtained.

关键词

Nash微分博弈 / 奇异随机系统 / Riccati方程 / 随机Missing dimension or its units for \kern 控制.

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曹铭 , 朱怀念 , 张成科 , 程硕. 奇异随机Markov跳变系统的N人Nash博弈问题. 系统科学与数学, 2017, 37(3): 700-712. https://doi.org/10.12341/jssms13096
CAO Ming , ZHU Huainian , ZHANG Chengke , CHENG Shuo. Nash Games of Singular Stochastic Markov Jump Systems with \bmN Decision Makers. Journal of Systems Science and Mathematical Sciences, 2017, 37(3): 700-712 https://doi.org/10.12341/jssms13096
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