  This paper addresses novel consensus problems in the presence of adversaries
that can move within the network and induce faulty behaviors in the attacked
agents. By adopting several mobile adversary models from the computer science
literature, we develop protocols which can mitigate the influence of such
malicious agents. The algorithms follow the class of mean subsequence reduced
(MSR) algorithms, under which agents ignore the suspicious values received from
neighbors during their state updates. Different from the static adversary
models, even after the adversaries move away, the infected agents may remain
faulty in their values, whose effects must be taken into account. We develop
conditions on the network structures for both the complete and non-complete
graph cases, under which the proposed algorithms are guaranteed to attain
resilient consensus. Extensive simulations are carried out over random graphs
to verify the effectiveness of our approach under uncertainties in the systems.

Systems and Control;Distributed, Parallel, and Cluster Computing;Systems and Control