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MIXED EQUILIBRIUM SOLUTION OF TIME-INCONSISTENT STOCHASTIC LINEAR-QUADRATIC PROBLEM

文献类型：期刊论文

作者Ni, Yuan-Hua2; Li, Xun3; Zhang, Ji-Feng1,4; Krstic, Miroslav5
刊名SIAM JOURNAL ON CONTROL AND OPTIMIZATION
出版日期2019
卷号57期号:1页码:533-569
关键词time inconsistency stochastic linear-quadratic optimal control mean-field optimal control forward-backward stochastic difference equation equilibrium solution
ISSN号0363-0129
DOI10.1137/18M1177068
英文摘要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.
资助项目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研究方向Automation & Control Systems ; Mathematics
语种英语
WOS记录号WOS:000460129700021
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/33444]  
专题系统科学研究所
通讯作者Zhang, Ji-Feng
作者单位1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
2.Nankai Univ, Coll Artificial Intelligence, Tianjin 300350, Peoples R China
3.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China
4.Chinese Acad Sci, Acad Math & Syst Sci, Inst Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
5.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,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.

入库方式： OAI收割

来源：数学与系统科学研究院

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