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

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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.

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Authors and Affiliations

  1. College of Information and Electrical Engineering, Shandong University of Science and Technology, Qingdao Shandong, 266510, China

    Huiying Sun, Liuyang Jiang & Weihai Zhang

Authors
  1. Huiying Sun
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  2. Liuyang Jiang
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  3. Weihai Zhang
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Corresponding author

Correspondence to Huiying Sun.

Additional information

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).

Huiying SUN received her M.S. degree from Qingdao University of Science and Technology and Ph.D. degree from the Ocean University of China, in 2004 and 2007, respectively. She is currently an associate professor of Shandong University of Science and Technology. Her main research interests include linear optimal control and stochastic systems.

Liuyang JIANG received her B.S. degree in Electrical Engineering from Qingdao Technological University in 2004. Since September 2009, she has been pursuing her M.S. degree in the Shandong University of Science and Technology. Her main research interests include linear optimal control and stochastic systems.

Weihai ZHANG received his M.S. degree from Hangzhou University, and Ph.D. degree from Zhejiang University, Hangzhou, China, in 1994 and 1998, respectively. From August 1998 to May 2001, he worked at Shandong Institute of Light Industry as an associate professor. He was a postdoctoral researcher from May 2001 to July 2003 at National Tsinghua University, Hsinchu, Taiwan. He is currently a professor of Shandong University of Science and Technology. His research interests include linear and nonlinear stochastic optimal control, robust H-infinity control and stochastic stability.

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Sun, H., Jiang, L. & Zhang, W. Infinite horizon linear quadratic differential games for discrete-time stochastic systems. J. Control Theory Appl. 10, 391–396 (2012). https://doi.org/10.1007/s11768-012-1004-z

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  • DOI: https://doi.org/10.1007/s11768-012-1004-z

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