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Consensus problems in networks of agents with switching topology and time-delays

Olfati-Saber, Reza and Murray, Richard M. (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Transactions on Automatic Control, 49 (9). pp. 1520-1533. ISSN 0018-9286. http://resolver.caltech.edu/CaltechAUTHORS:OLFieeetac04

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Abstract

In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.


Item Type:Article
Additional Information:© Copyright 2004 IEEE. Reprinted with permission. Manuscript received May 19, 2003; revised November 30, 2003. [Posted online: 2004-09-13] Recommended by Guest Editors P. Antsaklis and J. Bailleiul. This work was supported in part by the Air Force Office of Scientific Research under Grant F49620-01-1-0361 and by the Defense Advanced Research Projects Agency under Grant F33615-98-C-3613.
Subject Keywords:Algebraic graph theory, consensus problems, digraph theory, graph Laplacians, networks of autonomous agents, networks with time-delays, switching systems
Record Number:CaltechAUTHORS:OLFieeetac04
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:OLFieeetac04
Alternative URL:http://dx.doi.org/10.1109/TAC.2004.834113
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5146
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:03 Oct 2006
Last Modified:26 Dec 2012 09:04

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