Dynamic Games for Stochastic Systems with Delay
Dynamic Games for Stochastic Systems with Delay
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DOI：
10.1002/asjc.686
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发表时间：
2013-09
影响因子：
2.4
通讯作者：
H. Mukaidani
中科院分区：
文献类型：
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作者：
H. Mukaidani
本文讨论了一类由伊藤随机微分方程控制的线性随机时滞系统的动态对策。Pareto和Nash策略是通过求解交叉耦合矩阵不等式来实现的。为了获得这些策略集，新的交叉耦合代数方程（CSAE）的基础上的Karush-库恩-塔克（KKT）条件，构成必要条件。值得注意的是，状态反馈策略可以通过递归求解线性矩阵不等式（LMI）得到。最后，一个数值例子表明所提出的方法的有效性和所获得的成本范围。
This paper discusses dynamic games for a class of linear stochastic delay systems governed by Itô's stochastic differential equation. The Pareto and Nash strategies are developed by solving cross‐coupled matrix inequalities. To obtain these strategy sets, new cross‐coupled algebraic equations (CSAEs) are established on the basis of the Karush‐Kuhn‐Tucker (KKT) conditions, which constitute the necessary conditions. It is noteworthy that the state feedback strategies can be obtained by solving the linear matrix inequality (LMI) recursively. Finally, a numerical example showing the effectiveness of the proposed methods and the attained cost bounds is described.