Discrete-time mean-field Stochastic linear-quadratic optimal control problems, II: Infinite horizon case

doi:10.1016/j.automatica.2015.04.002

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	Discrete-time mean-field Stochastic linear-quadratic optimal control problems, II: Infinite horizon case
	Ni, Yuan-Hua 1,2; Elliott, Robert 3,4; Li, Xun 5
	2015-07-01
发表期刊	AUTOMATICA
ISSN	0005-1098
卷号	57 页码:65-77
摘要	This paper first presents results on the equivalence of several notions of L-2-stability for linear mean-field stochastic difference equations with random initial value. Then, it is shown that the optimal control of a mean-field linear quadratic optimal control with an infinite time horizon uniquely exists, and the optimal control can be expressed as a linear state feedback involving the state and its mean, via the minimal nonnegative definite solution of two coupled algebraic Riccati equations. As a byproduct, the open-loop L-2-stabilizability is proved to be equivalent to the closed-loop L-2-stabilizability. Moreover, the minimal nonnegative definite solution, the maximal solution, the stabilizing solution of the algebraic Riccati equations and their relations are carefully investigated. Specifically, it is shown that the maximal solution is employed to construct the optimal control and value function to another infinite time horizon mean-field linear quadratic optimal control. In addition, the maximal solution being the stabilizing solution, is completely characterized by properties of the coefficients of the controlled system. This enriches the existing theory about stochastic algebraic Riccati equations. Finally, the notion of exact detectability is introduced with its equivalent characterization of stochastic versions of the Popov-Belevitch-Hautus criteria. It is then shown that the minimal nonnegative definite solution is the stabilizing solution if and only if the uncontrolled system is exactly detectable. (C) 2015 Elsevier Ltd. All rights reserved.
关键词	Stochastic linear quadratic optimal control Mean-field theory Generalized algebraic Riccati equation
DOI	10.1016/j.automatica.2015.04.002
语种	英语
资助项目	National Natural Science Foundation of China[11101303] ; National Natural Science Foundation of China[11471242] ; China Postdoctoral Science Foundation[2014M560128] ; China Scholarship Council[201308120011] ; Australian Research Council[DP0877639] ; Natural Sciences and Engineering Research Council of Canada ; Hong Kong RGC[GRF520412] ; Hong Kong RGC[GRF15209614]
WOS研究方向	Automation & Control Systems ; Engineering
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000356746500009
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/20192
专题	中国科学院数学与系统科学研究院
通讯作者	Ni, Yuan-Hua
作者单位	1.Tianjin Polytech Univ, Sch Sci, Dept Math, Tianjin 300160, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 3.Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia 4.Univ Calgary, Haskayne Sch Business, Calgary, AB, Canada 5.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Ni, Yuan-Hua,Elliott, Robert,Li, Xun. Discrete-time mean-field Stochastic linear-quadratic optimal control problems, II: Infinite horizon case[J]. AUTOMATICA,2015,57:65-77.
APA	Ni, Yuan-Hua,Elliott, Robert,&Li, Xun.(2015).Discrete-time mean-field Stochastic linear-quadratic optimal control problems, II: Infinite horizon case.AUTOMATICA,57,65-77.
MLA	Ni, Yuan-Hua,et al."Discrete-time mean-field Stochastic linear-quadratic optimal control problems, II: Infinite horizon case".AUTOMATICA 57(2015):65-77.