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Discrete-time mean-field Stochastic linear-quadratic optimal control problems, II: Infinite horizon case
Ni, Yuan-Hua1,2; Elliott, Robert3,4; Li, Xun5
2015-07-01
Source PublicationAUTOMATICA
ISSN0005-1098
Volume57Pages:65-77
AbstractThis 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.
KeywordStochastic linear quadratic optimal control Mean-field theory Generalized algebraic Riccati equation
DOI10.1016/j.automatica.2015.04.002
Language英语
Funding ProjectNational 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 Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000356746500009
PublisherPERGAMON-ELSEVIER SCIENCE LTD
Citation statistics
Cited Times:26[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/20192
Collection中国科学院数学与系统科学研究院
Affiliation1.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
Recommended Citation
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.
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