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This work considers the problem of resilient consensus where stochasticvalues of trust between agents are available. Specifically, we derive a unifiedmathematical framework to characterize convergence, deviation of the consensusfrom the true consensus value, and expected convergence rate, when there existsadditional information of trust between agents. We show that under certainconditions on the stochastic trust values and consensus protocol: 1) almostsure convergence to a common limit value is possible even when malicious agentsconstitute more than half of the network connectivity, 2) the deviation of theconverged limit, from the case where there is no attack, i.e., the trueconsensus value, can be bounded with probability that approaches 1exponentially, and 3) correct classification of malicious and legitimate agentscan be attained in finite time almost surely. Further, the expected convergencerate decays exponentially with the quality of the trust observations betweenagents.

Characterizing Trust and Resilience in Distributed Consensus for Cyberphysical Systems