Convergence Speed in Distributed Consensus and Control
Optimization and Control
2011-06-13 v2 Systems and Control
Abstract
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.
Cite
@article{arxiv.math/0612682,
title = {Convergence Speed in Distributed Consensus and Control},
author = {Alex Olshevsky and John N. Tsitsiklis},
journal= {arXiv preprint arXiv:math/0612682},
year = {2011}
}