On the geometry of consensus algorithms with application to distributed termination in higher dimension

James Melbourne, Govind Saraswat, Vivek Khatana, Sourav Patel, Murti V. Salapaka

Research output: Contribution to journalConference articlepeer-review

2 Scopus citations

Abstract

We present insights into the geometry of the ratio consensus algorithm that lead to finite time distributed stopping criteria for the algorithm in higher dimension. In particular we show that the polytopes of network states indexed by time form a nested sequence. This monotonicity allows the construction of a distributed algorithm that terminates in finite time when applied to consensus problems in any dimension and guarantees the convergence of the consensus algorithm in norm, within any given tolerance. The practical utility of the algorithm is illustrated through MATLAB simulations.

Original languageEnglish (US)
Pages (from-to)2951-2956
Number of pages6
JournalIFAC-PapersOnLine
Volume53
Issue number2
DOIs
StatePublished - 2020
Event21st IFAC World Congress 2020 - Berlin, Germany
Duration: Jul 12 2020Jul 17 2020

Bibliographical note

Funding Information:
This work is supported by Advanced Research Projects Agency-Energy OPEN through the project titled "Rapidly Viable Sustained Grid" via grant no. DE-AR0001016.

Publisher Copyright:
© 2020 Elsevier B.V.. All rights reserved.

Keywords

  • Convex hull
  • Distributed consensus
  • High-dimensional state algorithms
  • Multi-agent systems
  • Network-based computing systems

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