On Communication Requirements for Multi-agent Consensus Seeking

L. Fang, P. Antsaklis

Networked Embedded Sensing and Control, Proceedings of Workshop NESC’05
University of Notre Dame, USA, October 17-18, 2005
Panos Antsaklis and Paulo Tabuada (Eds.)
Lecture Notes in Control and Information Sciences (LNCIS) 331, pp. 53-68, Springer 2006.

Abstract—Several consensus protocols have been proposed in the literature and their convergence properties studied via a variety of methods. In all these methods, the communication topologies play a key role in the convergence of consensus processes. The goal of this paper is two fold. The first goal is to explore communication topologies, as implied by the communication assumptions, that lead to consensus among agents. For this, we examine several important results in the literature and focus on different classes of communication assumptions being made, such as synchronism, connectivity, and direction of communication. In the latter part of this paper, we utilize iteration graphs to unify various consensus results. Based on asynchronous iteration methods for nonlinear paracontractions, we establish a new result which shows that consensus is reachable under directional, time-varying and asynchronous topologies with nonlinear protocols. In particular, the iteration graph concept proves to be fundamental in understanding the convergence of consensus processes.

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