Infinite horizon linear quadratic differential games for discrete-time stochastic systems

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• 作者：Huiying Sun ; Liuyang Jiang ; Weihai Zhang
• 关键词：Discrete ; time stochastic systems ; Exact observability ; Exact detectability ; Differential games ; Nash equilibrium
• 刊名：Control Theory and Technology
• 出版年：2012
• 出版时间：August 2012
• 年：2012
• 卷：10
• 期：3
• 页码：391-396
• 全文大小：185 KB
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• 作者单位：Huiying Sun (1)
  Liuyang Jiang (1)
  Weihai Zhang (1)
  
  1. College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao Shandong, 266510, China
  
• 刊物类别：Control; Systems Theory, Control; Optimization; Computational Intelligence; Complexity; Control, Rob
• 刊物主题：Control; Systems Theory, Control; Optimization; Computational Intelligence; Complexity; Control, Robotics, Mechatronics;
• 出版者：South China University of Technology and Academy of Mathematics and Systems Science, CAS
• ISSN：2198-0942

文摘

This paper deals with the infinite horizon linear quadratic (LQ) differential games for discrete-time stochastic systems with both state and control dependent noise. The Popov-Belevitch-Hautus (PBH) criteria for exact observability and exact detectability of discrete-time stochastic systems are presented. By means of them, we give the optimal strategies (Nash equilibrium strategies) and the optimal cost values for infinite horizon stochastic differential games. It indicates that the infinite horizon LQ stochastic differential games are associated with four coupled matrix-valued equations. Furthermore, an iterative algorithm is proposed to solve the four coupled equations. Finally, an example is given to demonstrate our results. Keywords Discrete-time stochastic systems Exact observability Exact detectability Differential games Nash equilibrium