Multi-Agent Resilient Consensus under Intermittent Faulty and Malicious Transmissions (Extended Version)

Abstract

In this work, we consider the consensus problem in which legitimate agents share their values over an undirected communication network in the presence of malicious or faulty agents. Different from the previous works, we characterize the conditions that generalize to several scenarios such as intermittent faulty or malicious transmissions, based on trust observations. As the standard trust aggregation approach based on a constant threshold fails to distinguish intermittent malicious/faulty activity, we propose a new detection algorithm utilizing time-varying thresholds and the random trust values available to legitimate agents. Under these conditions, legitimate agents almost surely determine their trusted neighborhood correctly with geometrically decaying misclassification probabilities. We further prove that the consensus process converges almost surely even in the presence of malicious agents. We also derive the probabilistic bounds on the deviation from the nominal consensus value that would have been achieved with no malicious agents in the system. Numerical results verify the convergence among agents and exemplify the deviation under different scenarios.