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HuainianZHU,ChengkeZHANG
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(School of Management, Guangdong University of Technology;School of Economics & Commence, Guangdong University of Technology)
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Received:September 12, 2011Revised:December 14, 2012
基金项目:This work was supported by the National Natural Science Foundation of China (No. 71171061) and the Natural Science Foundation of Guangdong Province (No. S2011010004970).
Infinite time horizon nonzero-sum linear quadratic stochastic differential games with state and control-dependent noise
Huainian ZHU,Chengke ZHANG
(School of Management, Guangdong University of Technology;School of Economics & Commence, Guangdong University of Technology)
Abstract:
This paper discusses the infinite time horizon nonzero-sum linear quadratic (LQ) differential games of stochastic systems governed by Itˆo’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.
Key words:  Stochastic system  Differential games  Stochastic H-two/H-infinity control