Resilient Consensus without Finite Time Detection Guarantees

Abstract

This paper investigates the asymptotic convergence of consensus processes under random malicious attacks with generalized time-varying attack probabilities. Agents leverage trust observations to identify their legitimate neighbors, but these generalized attack probabilities do not render any finite-time detection guarantees. In the absence of a finite-time detection, we demonstrate convergence of the consensus process in probability and expectation using misclassification probability bounds. We show that the weight matrices converge to the ideal weight matrix (which would have been used in the absence of malicious agents) in probability, and the consensus dynamics for legitimate agents reaches an agreement in probability and expectation. Numerical simulations validate our theoretical findings for several attack probability sequences.