Abstract
We are concerned with the problem of achieving average consensus on fixed, undirected and connected graphs with an unknown graph topology. Motivated by Nesterov's accelerated gradient algorithm [1] [2], we describe a completely distributed consensus protocol that has a rate of convergence of $\mathcal{O}(q^{2k}/k^{2})$ , where $k$ is the iteration number and $q is dependent on the second largest eigenvalue modulus of weighting matrix constructed on the graph. By casting the protocol into a linear time-variant system, we show a dimension-free worst case convergence rate bound, that is, a rate independent of the scale of the network. We also discuss several convergence rate bounds for different choices of the weighting matrix in the protocol.
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