Distributed Stopping Criterion for Consensus in the Presence of Delays

Mangal Prakash; Saurav Talukdar; Sandeep Attree; Vikas Yadav; Murti V. Salapaka

doi:10.1109/TCNS.2019.2917151

Distributed Stopping Criterion for Consensus in the Presence of Delays

Mangal Prakash, Saurav Talukdar, Sandeep Attree, Vikas Yadav, Murti V. Salapaka

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

Linear consensus protocol is an iterative distributed algorithm with asymptotic convergence guarantees. This paper develops and analyzes an algorithm for agents running linear consensus iterations to detect convergence to consensus within a specified error tolerance in a distributed manner. The distributed stopping criterion allows for time-varying bounded delays in information transmission and reception between agents. The algorithm relies on distributively determining the maximum and minimum values held by the agents. This paper further develops an algorithm for average consensus that utilizes a distributive stopping criterion, based on maximum and minimum consensus, where no centralized coordination is needed on how each agent weights its neighbor's values. Here, the doubly stochastic assumption on the weight matrix is relaxed and only column stochasticity is needed. The effectiveness of the algorithms is demonstrated by simulations and a comparison with prior work in the literature. Moreover, the demonstration of the proposed algorithms on an experimental test bed of Raspberry-Pi agents communicating wirelessly validates its applicability and utility.

Original language	English (US)
Article number	8715396
Pages (from-to)	85-95
Number of pages	11
Journal	IEEE Transactions on Control of Network Systems
Volume	7
Issue number	1
DOIs	https://doi.org/10.1109/TCNS.2019.2917151
State	Published - Mar 2020

Bibliographical note

Funding Information:
Manuscript received November 25, 2018; revised December 2, 2018 and March 18, 2019; accepted May 2, 2019. Date of publication May 15, 2019; date of current version March 18, 2020. This work was supported by Advanced Research projects Agency-Energy (ARPA-E) Award DE-AR0000701. Recommended by Associate Editor L. Shi. (Mangal Prakash and Saurav Talukdar contributed equally to this work.) (Corresponding author: Murti V. Salapaka.) M. Prakash, S. Attree, and M. V. Salapaka are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:,[email protected]; attre002@umn. edu; [email protected]).

Publisher Copyright:
© 2014 IEEE.

Keywords

Approximate consensus
average consensus with delays
consensus with delays
maximum consensus
minimum consensus

Publisher link

10.1109/TCNS.2019.2917151

Find It

Find It at U of M Libraries

Cite this

@article{42370bb4ec5d4906b29da7f5405db795,

title = "Distributed Stopping Criterion for Consensus in the Presence of Delays",

abstract = "Linear consensus protocol is an iterative distributed algorithm with asymptotic convergence guarantees. This paper develops and analyzes an algorithm for agents running linear consensus iterations to detect convergence to consensus within a specified error tolerance in a distributed manner. The distributed stopping criterion allows for time-varying bounded delays in information transmission and reception between agents. The algorithm relies on distributively determining the maximum and minimum values held by the agents. This paper further develops an algorithm for average consensus that utilizes a distributive stopping criterion, based on maximum and minimum consensus, where no centralized coordination is needed on how each agent weights its neighbor's values. Here, the doubly stochastic assumption on the weight matrix is relaxed and only column stochasticity is needed. The effectiveness of the algorithms is demonstrated by simulations and a comparison with prior work in the literature. Moreover, the demonstration of the proposed algorithms on an experimental test bed of Raspberry-Pi agents communicating wirelessly validates its applicability and utility.",

keywords = "Approximate consensus, average consensus with delays, consensus with delays, maximum consensus, minimum consensus",

author = "Mangal Prakash and Saurav Talukdar and Sandeep Attree and Vikas Yadav and Salapaka, {Murti V.}",

note = "Funding Information: Manuscript received November 25, 2018; revised December 2, 2018 and March 18, 2019; accepted May 2, 2019. Date of publication May 15, 2019; date of current version March 18, 2020. This work was supported by Advanced Research projects Agency-Energy (ARPA-E) Award DE-AR0000701. Recommended by Associate Editor L. Shi. (Mangal Prakash and Saurav Talukdar contributed equally to this work.) (Corresponding author: Murti V. Salapaka.) M. Prakash, S. Attree, and M. V. Salapaka are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:,[email protected]; attre002@umn. edu; [email protected]). Publisher Copyright: {\textcopyright} 2014 IEEE.",

year = "2020",

month = mar,

doi = "10.1109/TCNS.2019.2917151",

language = "English (US)",

volume = "7",

pages = "85--95",

journal = "IEEE Transactions on Control of Network Systems",

issn = "2325-5870",

publisher = "IEEE CONTROL SYSTEMS SOCIETY",

number = "1",

}

TY - JOUR

T1 - Distributed Stopping Criterion for Consensus in the Presence of Delays

AU - Prakash, Mangal

AU - Talukdar, Saurav

AU - Attree, Sandeep

AU - Yadav, Vikas

AU - Salapaka, Murti V.

N1 - Funding Information: Manuscript received November 25, 2018; revised December 2, 2018 and March 18, 2019; accepted May 2, 2019. Date of publication May 15, 2019; date of current version March 18, 2020. This work was supported by Advanced Research projects Agency-Energy (ARPA-E) Award DE-AR0000701. Recommended by Associate Editor L. Shi. (Mangal Prakash and Saurav Talukdar contributed equally to this work.) (Corresponding author: Murti V. Salapaka.) M. Prakash, S. Attree, and M. V. Salapaka are with the Department of Electrical and Computer Engineering, University of Minnesota, Minneapolis, MN 55455 USA (e-mail:,[email protected]; attre002@umn. edu; [email protected]). Publisher Copyright: © 2014 IEEE.

PY - 2020/3

Y1 - 2020/3

N2 - Linear consensus protocol is an iterative distributed algorithm with asymptotic convergence guarantees. This paper develops and analyzes an algorithm for agents running linear consensus iterations to detect convergence to consensus within a specified error tolerance in a distributed manner. The distributed stopping criterion allows for time-varying bounded delays in information transmission and reception between agents. The algorithm relies on distributively determining the maximum and minimum values held by the agents. This paper further develops an algorithm for average consensus that utilizes a distributive stopping criterion, based on maximum and minimum consensus, where no centralized coordination is needed on how each agent weights its neighbor's values. Here, the doubly stochastic assumption on the weight matrix is relaxed and only column stochasticity is needed. The effectiveness of the algorithms is demonstrated by simulations and a comparison with prior work in the literature. Moreover, the demonstration of the proposed algorithms on an experimental test bed of Raspberry-Pi agents communicating wirelessly validates its applicability and utility.

AB - Linear consensus protocol is an iterative distributed algorithm with asymptotic convergence guarantees. This paper develops and analyzes an algorithm for agents running linear consensus iterations to detect convergence to consensus within a specified error tolerance in a distributed manner. The distributed stopping criterion allows for time-varying bounded delays in information transmission and reception between agents. The algorithm relies on distributively determining the maximum and minimum values held by the agents. This paper further develops an algorithm for average consensus that utilizes a distributive stopping criterion, based on maximum and minimum consensus, where no centralized coordination is needed on how each agent weights its neighbor's values. Here, the doubly stochastic assumption on the weight matrix is relaxed and only column stochasticity is needed. The effectiveness of the algorithms is demonstrated by simulations and a comparison with prior work in the literature. Moreover, the demonstration of the proposed algorithms on an experimental test bed of Raspberry-Pi agents communicating wirelessly validates its applicability and utility.

KW - Approximate consensus

KW - average consensus with delays

KW - consensus with delays

KW - maximum consensus

KW - minimum consensus

UR - http://www.scopus.com/inward/record.url?scp=85065988500&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85065988500&partnerID=8YFLogxK

U2 - 10.1109/TCNS.2019.2917151

DO - 10.1109/TCNS.2019.2917151

M3 - Article

AN - SCOPUS:85065988500

SN - 2325-5870

VL - 7

SP - 85

EP - 95

JO - IEEE Transactions on Control of Network Systems

JF - IEEE Transactions on Control of Network Systems

IS - 1

M1 - 8715396

ER -

Distributed Stopping Criterion for Consensus in the Presence of Delays

Abstract

Bibliographical note

Keywords

Publisher link

Find It

Other files and links

Fingerprint

Cite this