基于Wasserstein度量计算的高置信度攻击检测
High-Confidence Attack Detection via Wasserstein-Metric Computations
摘要：
研究了线性信息物理系统的传感器攻击与故障检测问题，系统噪声服从未知的光尾分布。我们提出了一种新的基于阈值的检测机制，采用Wasserstein度量，并保证系统性能具有高置信度，采用有限数量的测量。建议的检测器可能会产生错误警报率$Δ$在正常操作中，其中$Δ$可以被调整到任意小的基准分布，这是我们的机制的一部分。因此，所提出的检测器是敏感的传感器攻击和故障具有统计行为，这是不同于系统的噪声。我们量化了隐形攻击的影响-其目的是扰乱系统运行，同时产生与自然系统噪声一致的假警报-通过概率可达集。为了使我们的方法易于实现，我们提出了一个线性最优化问题，计算建议的检测措施和半定的程序，产生建议的可达集。
英文摘要：
This paper considers a sensor attack and fault detection problem for linear cyber-physical systems, which are subject to system noise that can obey an unknown light-tailed distribution. We propose a new threshold-based detection mechanism that employs the Wasserstein metric, and which guarantees system performance with high confidence employing a finite number of measurements. The proposed detector may generate false alarms with a rate $Δ$ in normal operation, where $Δ$ can be tuned to be arbitrarily small by means of a benchmark distribution which is part of our mechanism. Thus, the proposed detector is sensitive to sensor attacks and faults which have a statistical behavior that is different from that of the system's noise. We quantify the impact of stealthy attacks---which aim to perturb the system operation while producing false alarms that are consistent with the natural system's noise---via a probabilistic reachable set. To enable tractable implementation of our methods, we propose a linear optimization problem that computes the proposed detection measure and a semidefinite program that produces the proposed reachable set.
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