Evaluating Criticality of Nodes in Consensus Network Under False Data Injection Attack

Abstract

In this paper, a finite-duration, magnitude-bounded false data injection (FDI) attack on consensus network is considered. The aim of the attacker is to induce disagreement between nodes and consequently, influence the convergence of consensus algorithm. In order to measure the induced disagreement, a metric, namely induced terminal disagreement (ITD), is defined. The objective of this study is to determine the criticality of individual nodes in terms of the worst-case ITD resulting from attack on them. To achieve that, for every node, the closed-form expressions for the optimal attack input which results in the maximum ITD and the corresponding value of ITD, are obtained. Based on that, criticality ranks are assigned to all nodes. These ranks are beneficial in allocating security resources and designing resilient architecture. Further, the effect of varying attack duration on the worst-case ITDs and criticality ranks, is analyzed. Finally, it is shown that the criticality ranks of nodes have strong negative correlation with their degrees. A numerical example and simulations are presented to illustrate the proposed results.