Detection of Perfect Stealthy Attacks on Cyber-Physical Systems Subject to Measurement Quantizations: A Watermark-Based Strategy

In this paper, the attack detection problem is inves-tigated for a class of closed-loop systems subjected to unknown-but-bounded noises in the presence of stealthy attacks. The measurement outputs from the sensors are quantized before transmission. A specific type of perfect stealthy attack, which meets certain rather stringent conditions, is taken into account. Such attacks could be injected by adversaries into both the sensor-to-estimator and controller-to-actuator channels, with the aim of disrupting the normal data flow. For the purpose of defending against these perfect stealthy attacks, a novel scheme based on watermarks is developed. This scheme includes the injection of watermarks (applied to data prior to quantization) and the recovery of data (implemented before the data reaches the estimator). The watermark-based scheme is designed to be both time-varying and hidden from adversaries through incorporating a time-varying and bounded watermark signal. Subsequently, a watermark-based attack detection strategy is proposed which thoroughly considers the characteristics of perfect stealthy attacks, thereby ensuring that an alarm is activated upon the occurrence of such attacks. An example is provided to demonstrate the efficacy of the proposed mechanism for detecting attacks.