Resilient leaderless and leader–follower consensus over random networks through ℓ-hop communication

This paper studies the resilient consensus problems under $\ell$-hop communication over directed random networks. We develop novel multi-hop protocols to tackle both leaderless and leader–follower consensus with a single leader when the multiagent system is under both attack from Byzantine agents and failure of communication edges. Our unified framework features a multiple-input multiple-output system design, and generalizes the weighted mean subsequence reduced algorithms, in which extremal values in the $\ell$-hop neighborhood of a cooperative agent are censored based on the notion of minimum message cover. We establish conditions on dynamical network structures, under which secure consensus with vector states can be achieved in the sense of almost sure convergence.