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
	2018-09-01
发表期刊	IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN	0018-9286
卷号	63 期号:9 页码:2771-2786
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.
关键词	Forward-backward stochastic difference equation mean-field theory stochastic linear-quadratic optimal control time inconsistency
DOI	10.1109/TAC.2017.2776740
语种	英语
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
WOS类目	Automation & Control Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000443705900002
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30906
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.