Distributed Fault Detection for Cyber-Physical Systems With Application to Power Network System

In this article, we investigate the problem of distributed fault detection for a class of cyber-physical system whose physical layer consists of numerous subsystems, each modeled as a linear discrete-time system. Considering the influence of process noise and measurement noise, the state estimation of each subsystem is completed using a distributed Kalman filter (DKF), in which the one-step prediction is corrected not only by the local innovation but also by the measurement errors of the neighbors at the previous step. Leveraging the DKF, a local residual generator is designed for each subsystem. The parameters of the DKF are then determined by minimizing the estimation error and the upper bound of its covariance in the fault-free case, which ensures the robustness of the residual. Furthermore, by utilizing the instantaneous $T^{2}$ test statistic and the sliding window-based $T^{2}$ test statistic of the residual signals, the corresponding residual evaluation function and fault detection threshold are established to facilitate fault detection for each subsystem. In the proposed fault detection scheme, each subsystem only transmits information to its neighbors, ensuring that each subsystem can detect its faults in a distributed manner. Additionally, a sufficient condition is provided to guarantee the mean square boundedness of the estimation error in the fault-free case. Finally, a power network system is employed to demonstrate the effectiveness of the proposed scheme.