Convergence Speed in Distributed Consensus and Control

Details Convergence Speed in Distributed Consensus and Control Convergence Speed in Distributed Consensus and Control

2006-12-22

arxiv.org/abs/math/0612682v2

Mathematics

Optimization and Control

Scientific paper

We study the convergence speed of distributed iterative algorithms for the consensus and averaging problems, with emphasis on the latter. We first consider the case of a fixed communication topology. We show that a simple adaptation of a consensus algorithm leads to an averaging algorithm. We prove lower bounds on the worst-case convergence time for various classes of linear, time-invariant, distributed consensus methods, and provide an algorithm that essentially matches those lower bounds. We then consider the case of a time-varying topology, and provide a polynomial-time averaging algorithm.

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