Low complexity resilient consensus in networked multi-agent systems with adversaries

Recently, many applications have arisen in distributed control that require consensus protocols. Concurrently, we have seen a proliferation of malicious attacks on large-scale distributed systems. Hence, there is a need for (i) consensus problems that take into consideration the presence of adversaries and specify correct behavior through appropriate conditions on agreement and safety, and (ii) algorithms for distributed control applications that solve such consensus problems resiliently despite breaches in security. This paper addresses these issues by (i) defining the adversarial asymptotic agreement problem, which requires that the uncompromised agents asymptotically align their states while satisfying an invariant condition in the presence of adversaries, and (ii) by designing a low complexity consensus protocol, the Adversarial Robust Consensus Protocol (ARC-P), which combines ideas from distributed computing and cooperative control. Two types of omniscient adversaries are considered: (i) Byzantine agents can convey different state trajectories to different neighbors in the network, and (ii) malicious agents must convey the same information to each neighbor. For each type of adversary, sufficient conditions are provided that ensure ARC-P guarantees the agreement and safety conditions in static and switching network topologies, whenever the number of adversaries in the network is bounded by a constant. The conservativeness of the conditions is examined, and the conditions are compared to results in the literature.