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Distributed Computation of Linear Matrix Equations: An Optimization Perspective
Zeng, Xianlin1; Liang, Shu2; Hong, Yiguang3; Chen, Jie4
2019-05-01
Source PublicationIEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN0018-9286
Volume64Issue:5Pages:1858-1873
AbstractThis 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.
KeywordConstrained convex optimization distributed computation least squares solution linear matrix equation substitutional decomposition
DOI10.1109/TAC.2018.2847603
Language英语
Funding ProjectNational 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 Research AreaAutomation & Control Systems ; Engineering
WOS SubjectAutomation & Control Systems ; Engineering, Electrical & Electronic
WOS IDWOS:000466226500007
PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/34914
Collection系统科学研究所
Corresponding AuthorZeng, Xianlin
Affiliation1.Beijing Inst Technol, Sch Automat, Key Lab Intelligent Control & Decis Complex Syst, Beijing 100081, Peoples R China
2.Univ Sci & Technol Beijing, Sch Automat & Elect Engn, Minist Educ, Key Lab Knowledge Automat Ind Proc, Beijing 100083, Peoples R China
3.Chinese Acad Sci, Key Lab Syst & Control, Acad Math & Syst Sci, Beijing 100190, 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
Recommended Citation
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.
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