Distributed average consensus with least-mean-square deviation

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 averag...

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Bibliographic Details
Published inJournal of parallel and distributed computing Vol. 67; no. 1; pp. 33 - 46
Main Authors Xiao, Lin, Boyd, Stephen, Kim, Seung-Jean
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 2007
Elsevier
Subjects
Applied sciences
Computer science; control theory; systems
Computer systems and distributed systems. User interface
Convex optimization
Distributed average consensus
Edge-transitive graphs
Exact sciences and technology
Least-mean-square
Software
Edge-transitive graphs
Convex optimization
Distributed average consensus
Least-mean-square
Additive noise
Autonomous system
Edge(graph)
Weighted average
Probabilistic approach
Coordination
Transitive graph
Mobility
Updating
Global optimum
Synchronization
Modeling
Convex programming
Steady state
Global solution
Consensus
Multiagent system
Least squares method
Load balancing
Mathematical programming
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Summary: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.
ISSN:0743-7315
1096-0848
DOI:10.1016/j.jpdc.2006.08.010