Bipartite Consensus for Multi-Agent Systems with Differential Privacy Constraint

This paper studies the differential privacy-preserving problem of discrete-time multi-agent systems (MASs) with antagonistic information, where the connected signed graph is structurally balanced. First, we introduce the bipartite consensus definitions in the sense of mean square and almost sure, respectively. Second, some criteria for mean square and almost sure bipartite consensus are derived, where the eventualy value is related to the gauge matrix and agents’ initial states. Third, we design the ε-differential privacy algorithm and characterize the tradeoff between differential privacy and system performance. Finally, simulations validate the effectiveness of the proposed algorithm.