Optimization-based attack against control systems with CUSUM-based anomaly detection

Security attacks on sensor data can deceive a control system and force the physical plant to reach an unwanted and potentially dangerous state. Therefore, attack detection mechanisms are employed in cyber-physical control systems to detect ongoing attacks, the most prominent one being a threshold-based anomaly detection method called CUSUM. Literature defines the maximum impact of stealth attacks as the maximum deviation in the plant's state that an undetectable attack can introduce, and formulates it as an optimization problem. This paper proposes an optimization-based attack with different saturation models, and it investigates how the attack duration significantly affects the impact of the attack on the state of the plant. We show that more dangerous attacks can be discovered when allowing saturation of the control system actuators. The proposed approach is compared with the geometric attack, showing how longer attack durations can lead to a greater impact of the attack while keeping the attack stealthy.