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Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control: From Finite Horizon to Infinite Horizon

文献类型：期刊论文

作者Ni, Yuan-Hua1,2; Li, Xun3; Zhang, Ji-Feng2
刊名IEEE TRANSACTIONS ON AUTOMATIC CONTROL
出版日期2016-11-01
卷号61期号:11页码:3269-3284
关键词Indefinite linear-quadratic optimal control mean-field theory stochastic system
ISSN号0018-9286
DOI10.1109/TAC.2015.2509958
英文摘要In this paper, the finite-horizon and the infinite-horizon indefinite mean-field stochastic linear-quadratic optimal control problems are studied. Firstly, the open-loop optimal control and the closed-loop optimal strategy for the finite-horizon problem are introduced, and their characterizations, difference and relationship are thoroughly investigated. The open-loop optimal control can be defined for a fixed initial state, whose existence is characterized via the solvability of a linear mean-field forward-backward stochastic difference equation with stationary conditions and a convexity condition. On the other hand, the existence of a closed-loop optimal strategy is shown to be equivalent to any one of the following conditions: the solvability of a couple of generalized difference Riccati equations, the finiteness of the value function for all the initial pairs, and the existence of the open-loop optimal control for all the initial pairs. It is then proved that the solution of the generalized difference Riccati equations converges to a solution of a couple of generalized algebraic Riccati equations. By studying another generalized algebraic Riccati equation, the existence of the maximal solution of the original ones is obtained together with the fact that the stabilizing solution is the maximal solution. Finally, we show that the maximal solution is employed to express the optimal value of the infinite-horizon indefinite mean-field linear-quadratic optimal control. Furthermore, for the question whether the maximal solution is the stabilizing solution, the necessary and the sufficient conditions are presented for several cases.
资助项目National Natural Science Foundation of China[11471242] ; National Natural Science Foundation of China[61227902] ; China Postdoctoral Science Foundation ; Hong Kong RGC Grants[520412] ; Hong Kong RGC Grants[15209614] ; National Key Basic Research Program of China (973 Program)[2014CB845301]
WOS研究方向Automation & Control Systems ; Engineering
语种英语
WOS记录号WOS:000389892000003
出版者IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/24269]  
专题系统科学研究所
通讯作者Ni, Yuan-Hua
作者单位1.Tianjin Polytech Univ, Sch Sci, Dept Math, Tianjin 300387, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
3.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,Li, Xun,Zhang, Ji-Feng. Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control: From Finite Horizon to Infinite Horizon[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2016,61(11):3269-3284.
APA Ni, Yuan-Hua,Li, Xun,&Zhang, Ji-Feng.(2016).Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control: From Finite Horizon to Infinite Horizon.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,61(11),3269-3284.
MLA Ni, Yuan-Hua,et al."Indefinite Mean-Field Stochastic Linear-Quadratic Optimal Control: From Finite Horizon to Infinite Horizon".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 61.11(2016):3269-3284.

入库方式： OAI收割

来源：数学与系统科学研究院

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