Stealthy FDI attacks on modified Kalman filtering in complex networks with non-Gaussian-Lévy noise

This paper investigates the problem of network security for stealthy false data injection (FDI) attacks under modified Kalman filtering (MKF) over complex networks with non-Gaussian-Lévy noise (NGLN). Initially, a modified Kalman filter (MKFR) is proposed to estimate system states, where the estimation function is related to the probabilistic characteristics of Lévy noise, and the saturation threshold is designed in relation to Lévy noise parameters. The upper bound of error covariance is obtained, and the boundedness of the upper bound is proven through the use of mathematical induction and iterative methods. Second, based on the MKF, this paper proposes a two-channel stealthy FDI attacks (TSFAs) strategy that is related only to the system model, which is injected into the sensor-to-controller (S-C) and controller-to-actuator (C-A) transmission channels at the same time. In addition, the attacker sets two MKFRs as observers to estimate the states of the target system, which are used to adjust the attack signal. Third, a sufficient condition is obtained that demonstrates the stability of the system. Meanwhile, TSFAs can avoid being detected by the residual-based detector to guarantee stealthiness. Finally, the effectiveness of the MKF is verified by the numerical simulation, and the stealthiness of the TSFAs and the impact on the system stability are also demonstrated.