Distributed resilient filtering for a class of nonlinear dynamical systems subject to hybrid cyber attacks

In this paper, the distributed resilient filtering issue is studied for a class of nonlinear dynamical systems subject to hybrid cyber attacks and gain disturbances. The gain perturbation could come from data rounding errors due to the fixed word length and is modeled by multiplicative noises. The addressed hybrid cyber attacks consist of both denial-of-service (DoS) attacks and deception attacks, in which the injected signal obeys a Gaussian mixture distribution. With the help of Kalman filtering theory, an optimally distributed filtering scheme is developed and the desired filter gain is derived by minimizing the filtering error covariance at each time instant. Furthermore, when the statistical information on DoS attacks is not available, the states of DoS attacks are identified in real-time by resorting to a maximum posterior probability estimation approach combined with the classical Bayesian rule. Based on the developed formulas and the identified state, a suboptimal distributed filtering algorithm is established to realize the state estimation. Finally, a simulation example shows the effectiveness of the proposed distributed resilient filtering algorithm.