Convergence of Gossip Algorithms for Consensus in Wireless Sensor Networks with Intermittent Links and Mobile Nodes

Abstract EN

We study the convergence of pairwise gossip algorithmsand broadcast gossip algorithms for consensus withintermittent links and mobile nodes.

By nonnegative matrixtheory and ergodicity coefficient theory, we prove gossip algorithmssurely converge as long as the graph is partitionallyweakly connected which, in comparison with existing analysis, isthe weakest condition and can be satisfied for most networks.

In addition we characterize the supremum for the mean squarederror of convergence as a function associated with the initial statesand the number of nodes.

Furthermore, on the condition that thegraph is partitionally strongly connected, the rate of convergenceis proved to be exponential and governed by the second largesteigenvalue of expected coefficient matrix.

For partitionally stronglyconnected digraphs, simulation results illustrate that gossipalgorithms actually converge, and broadcast gossip algorithmscan converge faster than pairwise gossip algorithms at the costof larger error of convergence.