Distributed Computation of Linear Matrix Equations: An Optimization Perspective

doi:10.1109/TAC.2018.2847603

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	Distributed Computation of Linear Matrix Equations: An Optimization Perspective
	Zeng, Xianlin 2; Liang, Shu 3; Hong, Yiguang1 ; Chen, Jie 4
刊名	IEEE TRANSACTIONS ON AUTOMATIC CONTROL
	2019-05-01
卷号	64 期号:5 页码:1858-1873
关键词	Constrained convex optimization distributed computation least squares solution linear matrix equation substitutional decomposition
ISSN号	0018-9286
DOI	10.1109/TAC.2018.2847603
英文摘要	This paper investigates the distributed computation of the well-known linear matrix equation in the form of AXB = F, with the matrices A, B, X, and F of appropriate dimensions, over multiagent networks from an optimization perspective. In this paper, we consider the standard distributed matrix-information structures, where each agent of the considered multiagent network has access to one of the subblock matrices of A, B, and F. To be specific, we first propose different decomposition methods to reformulate the matrix equations in standard structures as distributed constrained optimization problems by introducing substitutional variables; we show that the solutions of the reformulated distributed optimization problems are equivalent to least squares solutions to original matrix equations; and we design distributed continuous-time algorithms for the constrained optimization problems, even by using augmented matrices and a derivative feedback technique. Moreover, we prove the exponential convergence of the algorithms to a least squares solution to the matrix equation for any initial condition.
资助项目	National Key Research and Development Program of China[2016YFB0901902] ; National Natural Science Foundation of China[61333001] ; National Natural Science Foundation of China[61403231] ; National Natural Science Foundation of China[61603378] ; Fundamental Research Funds for the China Central Universities of USTB[FRF-TP-17-088A1] ; China Postdoctoral Science Foundation[2017M620020]
WOS研究方向	Automation & Control Systems ; Engineering
语种	英语
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
WOS记录号	WOS:000466226500007
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34913]
专题	系统科学研究所
通讯作者	Zeng, Xianlin
作者单位	1.Chinese Acad Sci, Key Lab Syst & Control, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Beijing Inst Technol, Sch Automat, Key Lab Intelligent Control & Decis Complex Syst, Beijing 100081, Peoples R China 3.Univ Sci & Technol Beijing, Sch Automat & Elect Engn, Minist Educ, Key Lab Knowledge Automat Ind Proc, Beijing 100083, Peoples R China 4.Beijing Inst Technol, Beijing Adv Innovat Ctr Intelligent Robots & Syst, Key Lab Biomimet Robots & Syst, Minist Educ, Beijing 100081, Peoples R China
推荐引用方式 GB/T 7714	Zeng, Xianlin,Liang, Shu,Hong, Yiguang,et al. Distributed Computation of Linear Matrix Equations: An Optimization Perspective[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL,2019,64(5):1858-1873.
APA	Zeng, Xianlin,Liang, Shu,Hong, Yiguang,&Chen, Jie.(2019).Distributed Computation of Linear Matrix Equations: An Optimization Perspective.IEEE TRANSACTIONS ON AUTOMATIC CONTROL,64(5),1858-1873.
MLA	Zeng, Xianlin,et al."Distributed Computation of Linear Matrix Equations: An Optimization Perspective".IEEE TRANSACTIONS ON AUTOMATIC CONTROL 64.5(2019):1858-1873.