Industrial control systems have been frequent targets of cyber attacks during the last decade. Adversaries can hinder the safe operation of these systems by tampering with their sensors and actuators, while ensuring that the monitoring systems are not able to detect such attacks in time. This paper presents methods to design and overcome stealthy attacks on linear time-invariant control systems that estimate their state using an interval observer, in the presence of unknown but bounded noise and perturbations. We analyze scenarios in which a malicious agent compromises the sensors and/or the actuators of the system with additive attack signals to steer the state estimate outside of the bounds provided by the interval observer. We first show that maximally disruptive attack sequences that remain undetected by a linear monitor can be computed recursively via linear programming. We then design an attack-resilient interval observer for the system’s state, identifying sufficient conditions on the sensor data for such an observer to be realizable. We propose a computational method to determine optimal observer gains using semi-definite programming and compute bounds for the unknown attack signal as well. In numerical simulations, we illustrate and compare the ability of such interval observers to still provide accurate estimates when under attack.

在过去十年中，工业控制系统经常成为网络攻击的目标。攻击者可以通过篡改传感器和执行器来阻碍这些系统的安全运行，同时确保监控系统无法及时检测到此类攻击。本文介绍了在存在未知但有界的噪声和扰动的情况下，设计和克服对线性时不变控制系统的隐身攻击的方法，这些系统使用区间观察器估计其状态。我们分析了恶意代理使用附加攻击信号破坏传感器和/或系统执行器的场景，以引导状态估计超出区间观察器提供的范围。我们首先表明，可以通过线性规划递归地计算线性监视器未检测到的最大破坏性攻击序列。然后，我们为系统状态设计了一个具有攻击弹性的区间观察器，识别传感器数据的充分条件，以便实现这样的观察器。我们提出了一种计算方法，使用半定规划确定最佳观察者增益，并计算未知攻击信号的界限。在数值模拟中，我们说明并比较了此类区间观察者在受到攻击时仍能提供准确估计的能力。我们提出了一种计算方法，使用半定规划确定最佳观察者增益，并计算未知攻击信号的界限。在数值模拟中，我们说明并比较了此类区间观察者在受到攻击时仍能提供准确估计的能力。我们提出了一种计算方法，使用半定规划确定最佳观察者增益，并计算未知攻击信号的界限。在数值模拟中，我们说明并比较了此类区间观察者在受到攻击时仍能提供准确估计的能力。