Time-Inconsistent Mean-Field Stochastic LQ Problem: Open-Loop Time-Consistent Control

doi:10.1109/TAC.2017.2776740

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	Time-Inconsistent Mean-Field Stochastic LQ Problem: Open-Loop Time-Consistent Control
	Ni, Yuan-Hua 1; Zhang, Ji-Feng2,3 ; Krstic, Miroslav 4
刊名	IEEE TRANSACTIONS ON AUTOMATIC CONTROL
	2018-09-01
卷号	63 期号:9 页码:2771-2786
关键词	Forward-backward stochastic difference equation mean-field theory stochastic linear-quadratic optimal control time inconsistency
ISSN号	0018-9286
DOI	10.1109/TAC.2017.2776740
英文摘要	This paper is concerned with the open-loop time-consistent solution of time-inconsistent mean-field stochastic linear-quadratic (LQ) optimal control. Different from standard stochastic linear-quadratic problems, both the system matrices and the weighting matrices are depending on the initial times, and the conditional expectations of the control and state enter quadratically into the cost functional. Such features will ruin Bellman's principle of optimality and result in the time inconsistency of optimal control. Based on the dynamical nature of the systems involved, a kind of open-loop time-consistent equilibrium control is investigated in this paper. It is shown that the existence of open-loop equilibrium control for a fixed initial pair is equivalent to the solvability of a set of forward-backward stochastic difference equations with stationary condition and convexity condition. By decoupling the forward-backward stochastic difference equations, necessary and sufficient conditions in terms of linear difference equations and generalized difference Riccati equations are given for the existence of open-loop equilibrium control for a fixed initial pair. Moreover, the existence of open-loop time-consistent equilibrium controls for all the initial pairs is shown to be equivalent to the solvability of a set of coupled constrained generalized difference Riccati equations and two sets of constrained linear difference equations.
资助项目	National Natural Science Foundation of China[11471242] ; National Natural Science Foundation of China[61773222] ; National Natural Science Foundation of China[61227902] ; National Key Basic Research Program of China (973 Program)[2014CB845301]
WOS研究方向	Automation & Control Systems ; Engineering
语种	英语
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
WOS记录号	WOS:000443705900002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/30945]
专题	系统科学研究所
通讯作者	Ni, Yuan-Hua
作者单位	1.Nankai Univ, Coll Comp & Control Engn, Tianjin 300350, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA
推荐引用方式 GB/T 7714	Ni, Yuan-Hua,Zhang, Ji-Feng,Krstic, Miroslav. Time-Inconsistent Mean-Field Stochastic LQ Problem: Open-Loop Time-Consistent Control[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2018,63(9):2771-2786.
APA	Ni, Yuan-Hua,Zhang, Ji-Feng,&Krstic, Miroslav.(2018).Time-Inconsistent Mean-Field Stochastic LQ Problem: Open-Loop Time-Consistent Control.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,63(9),2771-2786.
MLA	Ni, Yuan-Hua,et al."Time-Inconsistent Mean-Field Stochastic LQ Problem: Open-Loop Time-Consistent Control".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 63.9(2018):2771-2786.