Differential privacy bipartite consensus of multi-agent systems with switching topologies

This paper addresses the challenge of achieving bipartite consensus with rigorous privacy guarantees in multi-agent systems with antagonistic interactions and switching topologies. Existing methods lack effective solutions for privacy-preserving consensus under switching topologies and crucially fail to provide continuous protection of agent states throughout the consensus process, typically offering only initial state privacy guarantees. To fill these gaps, we propose a novel ε-differential privacy bipartite consensus (DPBC) protocol that incorporates noise injection capable of continuously protecting agent states at every time instant. The main contributions are threefold: (i) we establish a sensitivity upper bound theorem via dynamic sensitivity analysis, providing a principled foundation for noise calibration; (ii) we design a topology-adaptive noise injection mechanism that supports configurable privacy grades, allowing privacy levels to be adjusted on demand; (iii) we derive sufficient conditions, including graph connectivity, non-increasing step sizes, and bounded noise variance, to ensure both mean square bipartite consensus and ε-differential privacy under switching topologies, with continuous state protection at every time instant. Simulation results demonstrate that the proposed DPBC protocol maintains mean square bipartite consensus while provably preventing privacy leakage at every discrete time instant compared to baseline methods, outperforming existing approaches in terms of privacy assurance and scalability.