离散时间二人随机微分对策问题信息模式的数学描述  

Mathematical Description for Information Pattern of Discrete-Time Two-Person Stochastic Differential Games

作　　者：范红旗[1] 王胜[1] 付强[1] 

机构地区：[1]国防科技大学ATR实验室,湖南长沙410073

出　　处：《电子学报》2010年第6期1355-1361,共7页Acta Electronica Sinica

基　　金：973国家安全重大基础研究(No.51314);国防科技预研跨行业综合技术(No.51301050102)

摘　　要：在离散时间二人随机微分对策问题研究中,信息模式概念尚缺乏统一而准确的描述.针对这一问题,首先将Witsenhausen关于信息模式的相关概念应用到该问题,从数学上严格定义了信息模式及其相关概念,然后对几种典型信息模式的性质及相应对策问题最优解的结构形式作出了严格的证明.相关概念与性质为离散时间二人随机微分对策问题的研究提供了重要的理论工具.In the researches of discrete-time two-person stochastic differential games,the uniform and exact descriptions on information pattern are absent.To solve this problem,the mathematical definitions of information pattern and other related concepts are addressed firstly,by introducing Witsenhausen′s concepts about information pattern to the discrete-time two-person stochastic differential games.Then the properties of several typical information patterns and the structures of optimal control law of differential game under these information patterns are strictly proved.The concepts and theorems of the paper provide an important theoretical tool for the researches of discrete-time two-person stochastic differential games.

关 键 词：随机微分对策 信息模式 状态估计 最优控制 控制律 

分 类 号：TP273.1[自动化与计算机技术—检测技术与自动化装置]