KMS Of Academy of mathematics and systems sciences, CAS
| 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 Publication | IEEE TRANSACTIONS ON AUTOMATIC CONTROL
 |
| ISSN | 0018-9286 |
| Volume | 63Issue:9Pages:2771-2786 |
| Abstract | 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. |
| Keyword | Forward-backward stochastic difference equation mean-field theory stochastic linear-quadratic optimal control time inconsistency |
| DOI | 10.1109/TAC.2017.2776740 |
| Language | 英语 |
| Funding Project | 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 Research Area | Automation & Control Systems ; Engineering |
| WOS Subject | Automation & Control Systems ; Engineering, Electrical & Electronic |
| WOS ID | WOS:000443705900002 |
| Publisher | IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/30906 |
| Collection | 系统科学研究所 |
| Corresponding Author | Ni, Yuan-Hua |
| Affiliation | 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 |
| 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. |
| Files in This Item: | There are no files associated with this item. | |||||
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
Edit Comment