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

doi:10.1137/18M1177068

CSpace > 系统科学研究所

	MIXED EQUILIBRIUM SOLUTION OF TIME-INCONSISTENT STOCHASTIC LINEAR-QUADRATIC PROBLEM
	Ni, Yuan-Hua 1; Li, Xun 2; Zhang, Ji-Feng3,4 ; Krstic, Miroslav 5
	2019
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	57 期号:1 页码:533-569
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.
关键词	time inconsistency stochastic linear-quadratic optimal control mean-field optimal control forward-backward stochastic difference equation equilibrium solution
DOI	10.1137/18M1177068
语种	英语
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
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000460129700021
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	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.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
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.