Resilient real-valued consensus in spite of mobile malicious agents on directed graphs

This article addresses novel real-valued consensus problems in the presence of malicious 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 directed graph cases, under which the proposed algorithms are guaranteed to attain resilient consensus. The tolerance bound for network conditions becomes more strict as the adversaries are allowed to have more power. Extensive simulations are carried out over random graphs to verify the effectiveness of our approach when the information of the adversarial agents in terms of their models and numbers is unknown to the agents.