Abstract
This paper discusses the infinite time horizon nonzero-sum linear quadratic (LQ) differential games of stochastic systems governed by Itô’s equation with state and control-dependent noise. First, the nonzero-sum LQ differential games are formulated by applying the results of stochastic LQ problems. Second, under the assumption of mean-square stabilizability of stochastic systems, necessary and sufficient conditions for the existence of the Nash strategy are presented by means of four coupled stochastic algebraic Riccati equations. Moreover, in order to demonstrate the usefulness of the obtained results, the stochastic H-two/H-infinity control with state, control and external disturbance-dependent noise is discussed as an immediate application.
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This work was supported by the National Natural Science Foundation of China (No. 71171061) and the Natural Science Foundation of Guangdong Province (No. S2011010004970).
Huainian ZHU was born in 1985. He received his B.S. degree from North China Institute of Science and Technology in 2008, M.S. degree from Guangdong University of Technology in 2010. Currently, he is a Ph.D. candidate at the School of Management, Guangdong University of Technology. His research interests include management system engineering and game theory.
Chengke ZHANG was born in 1964. He is a professor at the School of Economics & Commence, Guangdong University of Technology. His research interests include system engineering, financial engineering, game theory and application.
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Zhu, H., Zhang, C. Infinite time horizon nonzero-sum linear quadratic stochastic differential games with state and control-dependent noise. J. Control Theory Appl. 11, 629–633 (2013). https://doi.org/10.1007/s11768-013-1182-3
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DOI: https://doi.org/10.1007/s11768-013-1182-3