KMS Of Academy of mathematics and systems sciences, CAS
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 Publication | AUTOMATICA |
ISSN | 0005-1098 |
Volume | 57Pages:65-77 |
Abstract | 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. |
Keyword | Stochastic linear quadratic optimal control Mean-field theory Generalized algebraic Riccati equation |
DOI | 10.1016/j.automatica.2015.04.002 |
Language | 英语 |
Funding Project | 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 Research Area | Automation & Control Systems ; Engineering |
WOS Subject | Automation & Control Systems ; Engineering, Electrical & Electronic |
WOS ID | WOS:000356746500009 |
Publisher | PERGAMON-ELSEVIER SCIENCE LTD |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/20192 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 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 |
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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