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Distributed average consensus with least-mean-square deviation

Xiao, Lin and Boyd, Stephen and Kim, Seung-Jean (2007) Distributed average consensus with least-mean-square deviation. Journal of Parallel and Distributed Computing, 67 (1). pp. 33-46. ISSN 0743-7315. doi:10.1016/j.jpdc.2006.08.010.

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We consider a stochastic model for distributed average consensus, which arises in applications such as load balancing for parallel processors, distributed coordination of mobile autonomous agents, and network synchronization. In this model, each node updates its local variable with a weighted average of its neighbors’ values, and each new value is corrupted by an additive noise with zero mean. The quality of consensus can be measured by the total mean-square deviation of the individual variables from their average, which converges to a steady-state value. We consider the problem of finding the (symmetric) edge weights that result in the least mean-square deviation in steady state. We show that this problem can be cast as a convex optimization problem, so the global solution can be found efficiently. We describe some computational methods for solving this problem, and compare the weights and the mean-square deviations obtained by this method and several other weight design methods.

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Additional Information:© 2006 Elsevier Inc. Received 27 May 2005; accepted 29 August 2006; available online 27 October 2006. We thank Devavrat Shah for discussions on the average consensus model with additive noises, and thank Anders Rantzer for discussions that helped identify an error in a previous draft.
Subject Keywords:Distributed average consensus; Least-mean-square; Convex optimization; Edge-transitive graphs
Issue or Number:1
Record Number:CaltechAUTHORS:20091117-142830676
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:16736
Deposited By: Jason Perez
Deposited On:18 Nov 2009 17:11
Last Modified:08 Nov 2021 23:29

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