Resilient Privacy-Preserving Consensus of Cooperative-Competitive Multi-Agent Systems under Byzantine Agents

This paper investigates secure and privacy-preserving consensus control for cooperative-competitive multi-agent systems (MASs) under Byzantine attacks. Considering that agents simultaneously interact cooperatively and competitively, we introduce a novel differential private (DP) resilient bipartite consensus protocol based on the Mean-Subsequence-Reduced (MSR) algorithm to defend against Byzantine agents. First, a resilient bipartite consensus controller incorporating Laplace noise is developed, which only works on competitive pairs of agents in the presence of potential eavesdroppers. Then, the convergence and privacy analyses demonstrate that the proposed algorithm can effectively preserve the privacy of initial states while simultaneously achieving resilient bipartite consensus. Furthermore, the privacy level is shown to be correlated with the minimum network degree. Finally, numerical simulations verify the effectiveness of the proposed results.