Abstract
This paper addresses the problem of resilient bipartite consensus for multi-agent networks in the presence of misbehaving nodes. The bipartite consensus problem was first studied by C. Altafini, and has been extensively studied in recent years. The interaction representing the communication between two agents is characterized by edge weights in a signed directed graph where the positive weight of an edge implies cooperation between the two agents while a negative one corresponds to antagonism. Resilient consensus problems without antagonistic interactions have been exhaustively studied, while the security problem of bipartite consensus, to the best of our knowledge, has not been studied yet. In this paper, we extend the resilient consensus problem to the case when antagonistic interactions exist. The developed results which are applicable for multi-agent systems with continuous-time dynamics shows that all normal nodes reach resilient bipartite consensus if the associated signed digraph is structurally balanced and has sufficient connectivity in terms of robustness. Numerical examples are provided to illustrate our results.
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