Multi-Agent Trustworthy Consensus under Random Dynamic Attacks

In this work, we study the consensus problem in which legitimate agents send their values over an undirected communication network in the presence of an unknown subset of malicious or faulty agents. In contrast to former works, we generalize and characterize the properties of consensus dynamics with dependent sequences of malicious transmissions with dynamic (time-varying) rates, based on not necessarily independent trust observations. We consider a detection algorithm utilizing stochastic trust observations available to legitimate agents. Under these conditions, legitimate agents almost surely classify their neighbors and form their trusted neighborhoods correctly with decaying misclassification probabilities. We further prove that the consensus process converges almost surely despite the existence of malicious agents. For a given value of failure probability, we characterize the deviation from the nominal consensus value ideally occurring when there are no malicious agents in the system. We also examine the convergence rate of the process in finite time. Numerical simulations show the convergence among agents and indicate the deviation under different attack scenarios.