KMS Of Academy of mathematics and systems sciences, CAS
MIXED EQUILIBRIUM SOLUTION OF TIME-INCONSISTENT STOCHASTIC LINEAR-QUADRATIC PROBLEM | |
Ni, Yuan-Hua1; Li, Xun2; Zhang, Ji-Feng3,4; Krstic, Miroslav5 | |
2019 | |
Source Publication | SIAM JOURNAL ON CONTROL AND OPTIMIZATION |
ISSN | 0363-0129 |
Volume | 57Issue:1Pages:533-569 |
Abstract | In this paper, we propose a novel equilibrium solution notion for the time-inconsistent stochastic linear-quadratic problem. This notion is called the mixed equilibrium solution, which consists of two parts: a pure-feedback-strategy part and an open-loop-control part. When the purefeedback-strategy part is zero or the open-loop-control part does not depend on the initial state, the mixed equilibrium solution reduces to the open-loop equilibrium control and the feedback equilibrium strategy, respectively. Using a maximum-principle-like methodology with forward-backward stochastic difference equations, a necessary and sufficient condition is established to characterize the existence of a mixed equilibrium solution. Then, by decoupling the forward-backward stochastic difference equations, three sets of difference equations, which together portray the existence of a mixed equilibrium solution, are obtained. Moreover, the case with a fixed time-state initial pair and the case with all the initial pairs are separately investigated. Furthermore, an example is constructed to show that the mixed equilibrium solution exists for all the initial pairs, although neither the open-loop equilibrium control nor the feedback equilibrium strategy exists for some initial pairs. |
Keyword | time inconsistency stochastic linear-quadratic optimal control mean-field optimal control forward-backward stochastic difference equation equilibrium solution |
DOI | 10.1137/18M1177068 |
Language | 英语 |
Funding Project | National Natural Science Foundation of China[61227902] ; National Natural Science Foundation of China[11471242] ; National Natural Science Foundation of China[61773222] ; National Natural Science Foundation of China[61877057] ; Hong Kong RGC[15224215] ; Hong Kong RGC[15255416] |
WOS Research Area | Automation & Control Systems ; Mathematics |
WOS Subject | Automation & Control Systems ; Mathematics, Applied |
WOS ID | WOS:000460129700021 |
Publisher | SIAM PUBLICATIONS |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/33444 |
Collection | 系统科学研究所 |
Corresponding Author | Zhang, Ji-Feng |
Affiliation | 1.Nankai Univ, Coll Artificial Intelligence, Tianjin 300350, Peoples R China 2.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 5.Univ Calif San Diego, Dept Mech & Aerosp Engn, La Jolla, CA 92093 USA |
Recommended Citation GB/T 7714 | Ni, Yuan-Hua,Li, Xun,Zhang, Ji-Feng,et al. MIXED EQUILIBRIUM SOLUTION OF TIME-INCONSISTENT STOCHASTIC LINEAR-QUADRATIC PROBLEM[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2019,57(1):533-569. |
APA | Ni, Yuan-Hua,Li, Xun,Zhang, Ji-Feng,&Krstic, Miroslav.(2019).MIXED EQUILIBRIUM SOLUTION OF TIME-INCONSISTENT STOCHASTIC LINEAR-QUADRATIC PROBLEM.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,57(1),533-569. |
MLA | Ni, Yuan-Hua,et al."MIXED EQUILIBRIUM SOLUTION OF TIME-INCONSISTENT STOCHASTIC LINEAR-QUADRATIC PROBLEM".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 57.1(2019):533-569. |
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