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We tackle the problem of a set of agents achieving resilient consensus in thepresence of attacked agents. We present a discrete-time reputation-basedconsensus algorithm for synchronous and asynchronous networks by developing alocal strategy where, at each time, each agent assigns a reputation (betweenzero and one) to each neighbor. The reputation is then used to weigh theneighbors' values in the update of its state. Under mild assumptions, we showthat: (i) the proposed method converges exponentially to the consensus of theregular agents; (ii) if a regular agent identifies a neighbor as an attackednode, then it is indeed an attacked node; (iii) if the consensus value of thenormal nodes differs from that of any of the attacked nodes' values, then thereputation that a regular agent assigns to the attacked neighbors goes to zero.Further, we extend our method to achieve resilience in the scenarios wherethere are noisy nodes, dynamic networks and stochastic node selection. Finally,we illustrate our algorithm with several examples, and we delineate someattacking scenarios that can be dealt by the current proposal but not by thestate-of-the-art approaches.

A Discrete-time Reputation-based Resilient Consensus Algorithm for Synchronous or Asynchronous Communications