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| Received:January 05, 2011Revised:July 02, 2011 |
| 基金项目:This work was supported by the National Natural Science Foundation of China (No. 61174078), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20103718110006), and A Project of Shandong Province Higher Educational Science and Technology Program (No. J12LN14). |
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| Infinite horizon linear quadratic differential games for discrete-time stochastic systems |
| Huiying SUN,Liuyang JIANG,Weihai ZHANG |
| (College of Information and Electrical Engineering, Shandong University of Science and Technology) |
| Abstract: |
| 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. |
| Key words: Discrete-time stochastic systems Exact observability Exact detectability Differential games Nash equilibrium |
