DELAYED OPTIMAL CONTROL OF STOCHASTIC LQ PROBLEM

doi:10.1137/16M1100897

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	DELAYED OPTIMAL CONTROL OF STOCHASTIC LQ PROBLEM
	Ni, Yuan-Hua 1; Yiu, Ka-Fai Cedric 2; Zhang, Huanshui 3; Zhang, Ji-Feng4,5
	2017
发表期刊	SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN	0363-0129
卷号	55 期号:5 页码:3370-3407
摘要	A stochastic linear-quadratic (LQ) problem with multiplicative noises and transmission delay is studied in this paper; this LQ problem does not require any definiteness constraint on the cost weighting matrices. From some abstract representations of the system and cost functional, the solvability of this LQ problem is characterized by some conditions with operator form. Based on these, necessary and sufficient conditions are derived for the case with a fixed time-state initial pair and the general case with all the time-state initial pairs. For both cases, a set of coupled discrete time Riccati-like equations can be derived to characterize the existence and the form of the delayed optimal control. In particular, for the general case with all the initial pairs, the existence of delayed optimal control is equivalent to the solvability of the Riccati-like equations with some algebraic constraints, and both of them are also equivalent to the solvability of a set of coupled linear matrix equality-inequalities. Note that both the constrained Riccati-like equations and the linear matrix equality-inequalities are introduced for the first time in the literature for the proposed LQ problem. Furthermore, the convexity and the uniform convexity of the cost functional are fully characterized via certain properties of the solution of the Riccati-like equations.
关键词	stochastic linear-quadratic optimal control transmission delay forward-backward stochastic difference equation convexity
DOI	10.1137/16M1100897
语种	英语
资助项目	National Natural Science Foundation of China[11471242] ; National Natural Science Foundation of China[31400005141601] ; National Natural Science Foundation of China[61773222] ; National Key Basic Research Program (973 Program) of China[2014CB845301] ; PolyU Grant G-YBKM ; AMSS-PolyU Joint Research Institute
WOS研究方向	Automation & Control Systems ; Mathematics
WOS类目	Automation & Control Systems ; Mathematics, Applied
WOS记录号	WOS:000416764700023
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/135
专题	系统科学研究所
通讯作者	Ni, Yuan-Hua
作者单位	1.Nankai Univ, Coll Comp & Control Engn, Tianjin 300350, Peoples R China 2.Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China 3.Shandong Univ, Sch Control Sci & Engn, Jinan 250061, Shandong, Peoples R China 4.Chinese Acad Sci, Key Lab Syst & Control, Inst Syst Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 5.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Ni, Yuan-Hua,Yiu, Ka-Fai Cedric,Zhang, Huanshui,et al. DELAYED OPTIMAL CONTROL OF STOCHASTIC LQ PROBLEM[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION,2017,55(5):3370-3407.
APA	Ni, Yuan-Hua,Yiu, Ka-Fai Cedric,Zhang, Huanshui,&Zhang, Ji-Feng.(2017).DELAYED OPTIMAL CONTROL OF STOCHASTIC LQ PROBLEM.SIAM JOURNAL ON CONTROL AND OPTIMIZATION,55(5),3370-3407.
MLA	Ni, Yuan-Hua,et al."DELAYED OPTIMAL CONTROL OF STOCHASTIC LQ PROBLEM".SIAM JOURNAL ON CONTROL AND OPTIMIZATION 55.5(2017):3370-3407.