Nash Strategy for Multiparameter Singularly Perturbed Markov Jump Stochastic Systems
Nash Strategy for Multiparameter Singularly Perturbed Markov Jump Stochastic Systems
复制标题
多参数奇异扰动马尔可夫跳跃随机系统的纳什策略
DOI：
10.1049/iet-cta.2011.0539
复制
发表时间：
2012
影响因子：
2.6
通讯作者：
Hiroaki Mukaidani and Toru Yamamoto
中科院分区：
文献类型：
--
作者：
H. Aota;T. Fukunaga;H. Nagamochi;Masahito Hasegawa (ed.);Shoichi Maruyama;四方順司;Hiroaki Mukaidani and Toru Yamamoto
研究了一类由伊藤微分方程控制的多参数奇摄动随机系统的Nash对策问题。首先，为了获得纳什均衡策略，交叉耦合随机代数Riccati方程（CSAREs）制定。此外，还得到了CSARE方程解存在的必要条件。值得注意的是，这是第一次，随机平衡的存在条件已导出的基础上的解决方案的CSARE集。在建立了CSAREs解的正定性渐近结构后，考虑了基于Newton方法和线性矩阵不等式（LMI）求解CSAREs的可行数值算法.最后通过数值算例验证了算法的有效性.
This study investigates Nash games for a class of multiparameter singularly perturbed stochastic systems governed by Itô’s differential equation with Markov jump parameters. First, in order to obtain Nash equilibrium strategies, cross-coupled stochastic algebraic Riccati equations (CSAREs) are formulated. Moreover, necessary condition for the existence of solution for CSAREs is also developed. It is noteworthy that this is the first time that conditions for the existence of stochastic equilibria have been derived based on the solutions of sets of CSAREs. After establishing an asymptotic structure with positive definiteness for CSAREs solutions, feasible numerical algorithms that are based on Newton’s method and the linear matrix inequality (LMI) for solving CSAREs is considered. Finally, the authors provide a numerical example to verify the efficiency of the proposed algorithms.