标题： 基于Wasserstein分布鲁棒可达性优化的网络物理系统虚假数据注入攻击检测方法 显示英文标题

标题： False Data-Injection Attack Detection in Cyber-Physical Systems: A Wasserstein Distributionally Robust Reachability Optimization Approach

摘要： 网络物理系统（CPS）是现代关键基础设施的基础骨干，因此确保其在针对网络攻击的安全性和弹性具有至关重要的意义。 本文解决了在虚假数据注入（FDI）攻击和由未知概率分布控制的随机扰动下设计异常检测器的挑战。 通过使用Wasserstein模糊集，这是一种在分布鲁棒优化（DRO）中广泛使用的数据驱动工具，我们首先提出了一种新的安全度量来处理扰动分布的缺失。 该度量是通过在分布鲁棒置信集内对由隐蔽FDI攻击和扰动引起的状态偏差进行渐近可达性分析而设计的。 然后，我们将检测器设计公式化为一个DRO问题，在一组分布下优化该安全度量并稳健地控制误报率。 这在扰动的鲁棒性和隐蔽攻击下的性能退化之间取得了权衡。 由于存在分布鲁棒机会约束，所产生的设计问题变成了一个具有挑战性的半无限规划问题。 我们推导了其精确但非凸的重新表述，并基于顺序优化开发了一个有效的解决方案算法。 最后，通过一个模拟的三水箱案例研究，展示了我们的设计在对抗未知扰动分布方面的有效性。 显示英文摘要

摘要： Cyber-physical system (CPS) is the foundational backbone of modern critical infrastructures, so ensuring its security and resilience against cyber-attacks is of pivotal importance. This paper addresses the challenge of designing anomaly detectors for CPS under false-data injection (FDI) attacks and stochastic disturbances governed by unknown probability distribution. By using the Wasserstein ambiguity set, a prevalent data-driven tool in distributionally robust optimization (DRO), we first propose a new security metric to deal with the absence of disturbance distribution. This metric is designed by asymptotic reachability analysis of state deviations caused by stealthy FDI attacks and disturbance in a distributionally robust confidence set. We then formulate the detector design as a DRO problem that optimizes this security metric while controlling the false alarm rate robustly under a set of distributions. This yields a trade-off between robustness to disturbance and performance degradation under stealthy attacks. The resulting design problem turns out to be a challenging semi-infinite program due to the existence of distributionally robust chance constraints. We derive its exact albeit non-convex reformulation and develop an effective solution algorithm based on sequential optimization. Finally, a case study on a simulated three-tank is illustrated to demonstrate the efficiency of our design in robustifying against unknown disturbance distribution.