In the intricate dance of multi-agent systems, achieving average consensus is not just vital--it is the backbone of their functionality. In conventional average consensus algorithms, all agents reach an agreement by individual calculations and sharing information with their respective neighbors. Nevertheless, the information interactions that occur in the communication network may make sensitive information be revealed. In this paper, we develop a new privacy-preserving average consensus method on unbalanced directed networks. Specifically, we ensure privacy preservation by carefully embedding randomness in mixing weights to confuse communications and introducing an extra auxiliary parameter to mask the state-updated rule in several initial iterations. In parallel, we exploit the intrinsic robustness of consensus dynamics to guarantee that the average consensus is precisely achieved. Theoretical results demonstrate that the designed algorithms can converge linearly to the exact average consensus value and can guarantee privacy preservation of agents against both honest-but-curious and eavesdropping attacks. The designed algorithms are fundamentally different compared to differential privacy based algorithms that enable privacy preservation via sacrificing consensus performance. Finally, numerical experiments validate the correctness of the theoretical findings.

翻译：在多智能体系统的复杂协同中，实现平均一致性不仅是关键——更是其功能发挥的基石。在传统的平均一致性算法中，所有智能体通过个体计算并与各自邻居共享信息来达成一致。然而，通信网络中发生的信息交互可能导致敏感信息泄露。本文针对非平衡有向网络，提出了一种新的隐私保护平均一致性方法。具体而言，我们通过以下方式确保隐私保护：在混合权重中精心嵌入随机性以混淆通信，并在若干初始迭代中引入额外的辅助参数来掩盖状态更新规则。同时，我们利用一致性动力学固有的鲁棒性来保证精确实现平均一致性。理论结果表明，所设计的算法能够线性收敛至精确的平均一致值，并能保护智能体隐私免受诚实但好奇型攻击与窃听攻击。与基于差分隐私、通过牺牲一致性性能来实现隐私保护的算法相比，本文所设计的算法存在本质区别。最后，数值实验验证了理论结果的正确性。