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A Generalized Gossip Algorithm on Convex Metric Spaces

A Generalized Gossip Algorithm on Convex Metric Spaces

Authors :
John S. Baras
Ion Matei
Christoforos Somarakis
Source :
IEEE Transactions on Automatic Control. 60:1175-1187
Publication Year :
2015
Publisher :
Institute of Electrical and Electronics Engineers (IEEE), 2015.

Abstract

A consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest. This problem can be generalized in the context of convex metric spaces that extend the standard notion of convexity. In this paper we introduce and analyze a randomized gossip algorithm for solving the generalized consensus problem on convex metric spaces, where the communication between agents is controlled by a set of Poisson counters. We study the convergence properties of the algorithm using stochastic calculus. In particular, we show that the distances between the states of the agents converge to zero with probability one and in the $r^{th} $ mean sense. In the special case of complete connectivity and uniform Poisson counters, we give upper bounds on the dynamics of the first and second moments of the distances between the states of the agents. In addition, we introduce instances of the generalized consensus algorithm for several examples of convex metric spaces together with numerical simulations.

Details

ISSN :
15582523 and 00189286
Volume :
60
Database :
OpenAIRE
Journal :
IEEE Transactions on Automatic Control
Accession number :
edsair.doi...........223d94b9fe0710a0b05347467bf3cdd1
Full Text :
https://doi.org/10.1109/tac.2014.2362989