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Time-Inconsistent Mean-Field Stochastic LQ Problem: Open-Loop Time-Consistent Control
Ni, Yuan-Hua1; Zhang, Ji-Feng2,3; Krstic, Miroslav4
2018-09-01
Source PublicationIEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN0018-9286
Volume63Issue:9Pages:2771-2786
AbstractThis 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.
KeywordForward-backward stochastic difference equation mean-field theory stochastic linear-quadratic optimal control time inconsistency
DOI10.1109/TAC.2017.2776740
Language英语
Funding ProjectNational 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 Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000443705900002
PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Citation statistics
Cited Times:2[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/30906
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
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