Characterizing Trust and Resilience in Distributed Consensus for Cyberphysical Systems

Abstract

This work considers the problem of resilient consensus, where stochastic values of trust between agents are available. Specifically, we derive a unified mathematical framework to characterize convergence, deviation of the consensus from the true consensus value, and expected convergence rate, when there exists additional information of trust between agents. We show that under certain conditions on the stochastic trust values and consensus protocol: First, almost sure convergence to a common limit value is possible even when malicious agents constitute more than half of the network connectivity; second, the deviation of the converged limit, from the case where there is no attack, i.e., the true consensus value, can be bounded with probability that approaches 1 exponentially; and third correct classification of malicious and legitimate agents can be attained in finite time almost surely. Furthermore, the expected convergence rate decays exponentially as a function of the quality of the trust observations between agents.