采用简约水印策略的信息物理系统欺骗攻击最快检测
Quickest Detection of Deception Attacks on Cyber-Physical Systems with a Parsimonious Watermarking Policy
AI总结：
针对信息物理系统数据欺骗攻击，本文提出动态规划驱动的简约双阈值水印策略，在误报率和控制成本约束下最小化平均检测延迟，并通过非线性更新理论与仿真验证。
摘要：
在控制输入中加入物理水印信号可以提高数据欺骗攻击的检测概率，但代价是增加控制成本。本文提出一种简约策略，用于在攻击不存在时减少水印事件的平均数量，从而降低控制成本。我们将系统建模为随机最优控制问题，并应用动态规划，在误报率（FAR）和控制成本增量具有固定上界的条件下最小化平均检测延迟（ADD）。最优解产生了关于攻击后验概率的双阈值策略；该后验概率由用于序贯变化检测的 Shiryaev 统计量导出，并假设变化点是服从几何分布的随机变量。我们应用非线性更新理论推导了 ADD 和 FAR 的近似表达式。文中还推导了攻击前加入水印的平均数量与控制成本增量之间的关系。我们设计了在控制成本增量固定时最大化 Kullback-Leibler 散度的最优水印。仿真研究对理论结果进行了说明和验证。
英文摘要：
The addition of a physical watermarking signal to the control input increases the detection probability of data deception attacks at the expense of increased control cost. In this paper, we propose a parsimonious policy to reduce the average number of watermarking events when the attack is not present, which in turn reduces the control cost. We model the system as a stochastic optimal control problem and apply the dynamic programming to minimize the average detection delay (ADD) for fixed upper bounds on false alarm rate (FAR) and increased control cost. The optimal solution results in a two threshold policy on the posterior probability of attack, which is derived from the Shiryaev statistics for sequential change detection assuming the change point is a random variable with a geometric distribution. We derive approximate expressions of ADD and FAR applying the non-linear renewal theory. The relationship between the average number of watermarking added before the attack and the increase in control cost is also derived. We design the optimal watermarking that maximizes the Kullback-Leibler divergence for a fixed increase in the control cost. Simulation studies are performed to illustrate and validate the theoretical results.
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