Attack Detection and Active Attack Defense for Cyber--Physical Systems via Zonotopic Observer and Reachability Analysis

This article concentrates on the attack detection and active attack defense strategies for discrete-time linear cyber-physical systems (CPSs) with unknown but bounded (UBB) disturbance and noise in the presence of both actuator and sensor attacks. First, a novel zonotopic observer is constructed to estimate the set-valued state and actuator attack by introducing augmentation techniques. To mitigate the effects of uncertainty and enhance estimation accuracy, the $H_{\infty }$ technique is introduced to construct the observer. Unlike most existing works, the constructed observer simultaneously estimates the system state and actuator attacks. Then, by combining the designed observer with reachability analysis, a set-valued abnormal detector and a residual-based abnormal detector are designed to detect actuator and sensor attacks, respectively. In addition, by incorporating the obtained state reachable sets and the $H_{\infty }$ technique, an active attack defense mechanism is designed to mitigate the impact of attacks on system performance. The proposed defense strategy does not introduce any performance loss in the absence of attacks. Finally, the superiority of the developed method is demonstrated by its application to a numerical simulation and an autonomous aircraft system.