Distributed Identification of the Most Critical Node for Average Consensus

Abstract

In present computer networks, cyber attacks, such as compromising and energy depleting attacks, can cause malfunction or even failure of nodes, and can be significantly harmful to the convergence property of the average consensus algorithms. In this paper, we aim to distributively find the most critical nodes in the sense that removing it causes the largest destruction to the converging speed of an average consensus algorithm among all the nodes. The algebraic connectivity is used to assess the destruction and thus the importance of a node. We design two methods to estimate the algebraic connectivity and analyze their bounds for the estimation error. Based on this, we propose a fully distributed algorithm for the nodes to iteratively find the most critical one. Simulation results demonstrate the effectiveness of our algorithm.