On Convergence Rate of Weighted-Averaging Dynamics for Consensus Problems

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

This paper investigates the weighted-Averaging dynamic for unconstrained and constrained consensus problems. Through the use of a suitably defined adjoint dynamic, quadratic Lyapunov comparison functions are constructed to analyze the behavior of weighted-Averaging dynamic. As a result, new convergence rate results are obtained that capture the graph structure in a novel way. In particular, the exponential convergence rate is established for unconstrained consensus with the exponent of the order of 1-O(1/(m\log-{2}m)) for special tree-like regular graphs. Also, the exponential convergence rate is established for constrained consensus over time-varying graphs, which nontrivially extends the existing result limited to the static graph case and the use of uniform weight matrices. Our main results are developed for directed graphs that are weakly connected, and we also provide statements regarding the rates in case of joint connectivity.

Original languageEnglish (US)
Article number7478088
Pages (from-to)766-781
Number of pages16
JournalIEEE Transactions on Automatic Control
Volume62
Issue number2
DOIs
StatePublished - Feb 1 2017
Externally publishedYes

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Keywords

  • Collaborative system
  • distributed weighted averaging
  • multi-Agent system
  • time-varying graphs

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Cite this

On Convergence Rate of Weighted-Averaging Dynamics for Consensus Problems. / Nedich, Angelia; Liu, Ji.

In: IEEE Transactions on Automatic Control, Vol. 62, No. 2, 7478088, 01.02.2017, p. 766-781.

Research output: Contribution to journalArticle

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