A Distributed Algorithm with Scalar States for Solving Linear Equations

Xuan Wang; Shaoshuai Mou; Brian D.O. Anderson

doi:10.1109/CDC.2018.8618967

A Distributed Algorithm with Scalar States for Solving Linear Equations

Xuan Wang, Shaoshuai Mou, Brian D.O. Anderson

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

5 Citations (Scopus)

Abstract

Based on a combination of consensus and conservation, the paper develops a distributed update for solving linear equations by multi-agent networks, in which each agent only knows just a small part of the overall equation and can only communicate with its nearby neighbors. In the proposed distributed update, each agent knows only two scalar entries of the defining matrix of the overall equation and controls just two scalar states. Given the underlying networks to be connected and undirected, the proposed distributed update enables agents to collaboratively achieve a solution to the overall equation. Analytical proof is provided for the exponential convergence of the proposed update, which is also validated by numerical simulations.

Original language	English
Title of host publication	2018 IEEE Conference on Decision and Control, CDC 2018
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2861-2865
Number of pages	5
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8618967
Publication status	Published - 2 Jul 2018
Externally published	Yes
Event	57th IEEE Conference on Decision and Control, CDC 2018 - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2018-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	57th IEEE Conference on Decision and Control, CDC 2018
Country/Territory	United States
City	Miami
Period	17/12/18 → 19/12/18

Access to Document

10.1109/CDC.2018.8618967

Cite this

Wang, X., Mou, S., & Anderson, B. D. O. (2018). A Distributed Algorithm with Scalar States for Solving Linear Equations. In 2018 IEEE Conference on Decision and Control, CDC 2018 (pp. 2861-2865). Article 8618967 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2018.8618967

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title = "A Distributed Algorithm with Scalar States for Solving Linear Equations",

abstract = "Based on a combination of consensus and conservation, the paper develops a distributed update for solving linear equations by multi-agent networks, in which each agent only knows just a small part of the overall equation and can only communicate with its nearby neighbors. In the proposed distributed update, each agent knows only two scalar entries of the defining matrix of the overall equation and controls just two scalar states. Given the underlying networks to be connected and undirected, the proposed distributed update enables agents to collaboratively achieve a solution to the overall equation. Analytical proof is provided for the exponential convergence of the proposed update, which is also validated by numerical simulations.",

author = "Xuan Wang and Shaoshuai Mou and Anderson, {Brian D.O.}",

note = "Publisher Copyright: {\textcopyright} 2018 IEEE.; 57th IEEE Conference on Decision and Control, CDC 2018 ; Conference date: 17-12-2018 Through 19-12-2018",

year = "2018",

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day = "2",

doi = "10.1109/CDC.2018.8618967",

language = "English",

series = "Proceedings of the IEEE Conference on Decision and Control",

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Wang, X, Mou, S & Anderson, BDO 2018, A Distributed Algorithm with Scalar States for Solving Linear Equations. in 2018 IEEE Conference on Decision and Control, CDC 2018., 8618967, Proceedings of the IEEE Conference on Decision and Control, vol. 2018-December, Institute of Electrical and Electronics Engineers Inc., pp. 2861-2865, 57th IEEE Conference on Decision and Control, CDC 2018, Miami, United States, 17/12/18. https://doi.org/10.1109/CDC.2018.8618967

A Distributed Algorithm with Scalar States for Solving Linear Equations. / Wang, Xuan; Mou, Shaoshuai; Anderson, Brian D.O.
2018 IEEE Conference on Decision and Control, CDC 2018. Institute of Electrical and Electronics Engineers Inc., 2018. p. 2861-2865 8618967 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2018-December).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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N2 - Based on a combination of consensus and conservation, the paper develops a distributed update for solving linear equations by multi-agent networks, in which each agent only knows just a small part of the overall equation and can only communicate with its nearby neighbors. In the proposed distributed update, each agent knows only two scalar entries of the defining matrix of the overall equation and controls just two scalar states. Given the underlying networks to be connected and undirected, the proposed distributed update enables agents to collaboratively achieve a solution to the overall equation. Analytical proof is provided for the exponential convergence of the proposed update, which is also validated by numerical simulations.

AB - Based on a combination of consensus and conservation, the paper develops a distributed update for solving linear equations by multi-agent networks, in which each agent only knows just a small part of the overall equation and can only communicate with its nearby neighbors. In the proposed distributed update, each agent knows only two scalar entries of the defining matrix of the overall equation and controls just two scalar states. Given the underlying networks to be connected and undirected, the proposed distributed update enables agents to collaboratively achieve a solution to the overall equation. Analytical proof is provided for the exponential convergence of the proposed update, which is also validated by numerical simulations.

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M3 - Conference contribution

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BT - 2018 IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 57th IEEE Conference on Decision and Control, CDC 2018

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A Distributed Algorithm with Scalar States for Solving Linear Equations

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