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International Conference on Complex Systems (ICCS2006)

Consensus problems on small world graphs: a structural study

Pedram Hovareshti
University of Maryland College Park

John Baras
Department of Elecectrical and Computer Engineering and the Institute for systems Research, University of Maryland College Park

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     Last modified: August 14, 2006

Note: To see a more complete version of this abstract, please go to http://necsi.org/events/iccs6/abstract/Iccs.pdf

Consensus problems arise in many instances of collaborative control
of multi-agent complex systems; where it is important for the
agents to act in coordination with the other agents. To reach
coordination, agents need to share information. In large groups of
agents the information sharing should be local in some sense, due
to energy limitation, reliability, and other constraints. A
consensus protocol is an iterative method that provides the group
with a common coordination variable. However, local information
exchange limits the speed of convergence of such protocols.
Therefore, in order to achieve high convergence speed, we should
be able to design appropriate network topologies. A reasonable
conjecture is that the small world graphs should result in good
convergence speed for consensus problems because their low average
pairwise path length should speed the diffusion of information in
the system. In this paper we address this conjecture by
simulations and also by studying the spectral properties of a
class of matrices corresponding to consensus problems on small
world graphs.

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