This paper proposes a distributed attack detection and mitigation technique based on distributed estimation over a multi-agent network, where the agents take partial system measurements susceptible to (possible) biasing attacks. In particular, we assume that the system is not locally observable via the measurements in the direct neighborhood of any agent. First, for performance analysis in the attack-free case, we show that the proposed distributed estimation is unbiased with bounded mean-square deviation in steady-state. Then, we propose a residual-based strategy to locally detect possible attacks at agents. In contrast to the deterministic thresholds in the literature assuming an upper bound on the noise support, we define the thresholds on the residuals in a probabilistic sense. After detecting and isolating the attacked agent, a system-digraph-based mitigation strategy is proposed to replace the attacked measurement with a new observationally-equivalent one to recover potential observability loss. We adopt a graph-theoretic method to classify the agents based on their measurements, to distinguish between the agents recovering the system rank-deficiency and the ones recovering output-connectivity of the system digraph. The attack detection/mitigation strategy is specifically described for each type, which is of polynomial-order complexity for large-scale applications. Illustrative simulations support our theoretical results.

中文翻译：

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分布式检测和缓解多代理网络上的偏见攻击

本文提出了一种基于多代理网络上的分布式估计的分布式攻击检测和缓解技术，其中代理采取易受（可能）偏置攻击的部分系统测量。特别是，我们假设系统不能通过任何代理的直接邻域中的测量在本地观察到。首先，对于无攻击情况下的性能分析，我们表明所提出的分布式估计是无偏的，在稳态下具有有界均方偏差。然后，我们提出了一种基于残差的策略来本地检测对代理的可能攻击。与假设噪声支持上限的文献中的确定性阈值相反，我们在概率意义上定义残差的阈值。在检测并隔离受攻击的代理后，提出了一种基于系统有向图的缓解策略，用新的观察等效的测量替换受攻击的测量，以恢复潜在的可观察性损失。我们采用图论方法根据代理的测量值对代理进行分类，以区分恢复系统秩缺陷的代理和恢复系统有向图输出连接性的代理。攻击检测/缓解策略针对每种类型进行了具体描述，对于大规模应用具有多项式阶复杂度。说明性模拟支持我们的理论结果。区分恢复系统秩缺陷的代理和恢复系统有向图的输出连接的代理。攻击检测/缓解策略针对每种类型进行了具体描述，对于大规模应用具有多项式阶复杂度。说明性模拟支持我们的理论结果。区分恢复系统秩缺陷的代理和恢复系统有向图的输出连接的代理。攻击检测/缓解策略针对每种类型进行了具体描述，对于大规模应用具有多项式阶复杂度。说明性模拟支持我们的理论结果。