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

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