AI 中文总结
研究多智能体系统中固有通信噪声能否保证隐私，通过建立通信噪声模型，设计分布式LQR机制，以保护智能体私有控制偏好实现编队跟踪，提供差分隐私保证，验证了理论结果及隐私 - 性能权衡。
AI 中文摘要
本文针对多智能体系统（MAS）提出了一种差分隐私分布式协同控制方案。与传统主动注入人工噪声进行隐私保护的方法不同，本文研究固有通信噪声能否本身作为一种自然隐私机制。通过纳入发射机扰动、接收机噪声、路径损耗衰减和对数正态阴影，为移动MAS建立了一个基于物理的通信噪声模型。由此产生的有效噪声方差取决于智能体间的状态差异，从而捕捉实际中出现的距离相关信号扰动。基于此模型，设计了一种分布式有限时域线性二次调节器（LQR）机制，以在保护智能体私有控制偏好的同时实现编队跟踪。所提出的隐私公式关注LQR加权矩阵的比率，而非保护整个局部成本函数。集合论敏感性分析表明，在所考虑的添加/删除邻接关系下，这种加权比率邻接公式产生的隐私边界比基于梯度的保护更不保守。理论分析表明，在合适的设计条件下，所提出的机制在无人工噪声注入的情况下，为无限时域上的加权比率提供有界累积（\(\epsilon\)，\(\delta\)）差分隐私保证。同时，协同跟踪误差几乎必然且在均方意义下收敛到一个有限随机极限，其期望保持有界。数值例子验证了理论结果，并说明了由此产生的隐私 - 性能权衡。
英文摘要
This paper proposes a differentially private distributed cooperative control scheme for multi-agent systems (MAS). Unlike conventional approaches that actively inject artificial noise for privacy protection, this work investigates whether inherent communication noise can itself serve as a natural privacy mechanism. A physically motivated communication-noise model is developed for mobile MAS by incorporating transmitter perturbation, receiver noise, path-loss attenuation, and log-normal shadowing. The resulting effective noise variance depends on inter-agent state differences, thereby capturing the distance-dependent signal perturbation arising in practice. Based on this model, a distributed finite-horizon Linear Quadratic Regulator (LQR) mechanism is designed to achieve formation tracking while protecting agents' private control preferences. Rather than protecting the full local cost function, the proposed privacy formulation focuses on the ratio of the LQR weighting matrices, which captures the trade-off between tracking accuracy and control effort when the quadratic cost structure is publicly known. A set-theoretic sensitivity analysis shows that this weighting-ratio adjacency formulation yields less conservative privacy bounds than gradient-based protection under the considered addition/removal adjacency relation. Theoretical analysis demonstrates that, under suitable design conditions, the proposed mechanism provides bounded cumulative (ε,δ)-differential privacy guarantees for the weighting ratios over an infinite horizon without artificial noise injection. Meanwhile, the cooperative tracking error is shown to converge almost surely and in mean square to a finite random limit, with its expectation remaining bounded. Numerical examples validate the theoretical results and illustrate the resulting privacy-performance trade-off.
