Averaging over general random networks
Kai Cai
IEEE Transactions on Automatic Control, vol. 57, no. 12, pp. 3186-3191, Dec. 2012
Keywords: Surplus-based averaging, distributed consensus, matrix perturbation theory, random networks/graphs
Abstract: This technical note studies the distributed averaging problem over general random networks, by means of augmenting state space. A general iterative scheme (with a certain structure) is proposed that is discrete-time, linear, and stochastic; its generality compared to the literature lies in that the weight matrices corresponding to the networks need not be column-stochastic, and the random process generating the update matrices need not be ergodic or i.i.d. It is then justified that the scheme achieves average consensus in the mean-square sense, which, in a special case, also implies averaging with probability one. A key technique to the justification is a matrix perturbation result, which describes the behavior of eigenvalues perturbed simultaneously by multiple parameters.
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