Bipartite Consensus in the Presence of Denial of Service Adversary

In this paper, we consider a Denial of Service (DoS) attack on a set of agents interacting over an undirected signed graph attempting to achieve linear bipartite consensus. In bipartite consensus, two clusters are formed, agents in each cluster converging to a final state which is negative of the other cluster's final state. The adversary seeks to slow down the bipartite consensus by a DoS type attack where the attacker has the capability to break a fixed maximum number of links at each time instant. The problem is formulated as an optimal control problem and the optimal strategy for the adversary is determined. The optimal strategy is provided as an algorithm and results are demonstrated with numerical simulations. Copyright (C) 2022 The Authors.