Recursive filtering with randomly occurring false data injection attacks

This paper is concerned with the recursive filter analysis and synthesis problem for a class of nonlinear systems with randomly occurring false data injection attacks. A novel randomly occurring attack model is established by using a Bernoulli binary distributed white sequence with the given probability. The aim of the addressed filtering problem is to design a recursive filter such that, there exists an upper bound for the filtering error covariance in the presence of nonlinearities and randomly occurring false data injection attacks. Moreover, such an upper bound is minimized at each sampling instant. By solving two Riccati-like difference equations, the filter gain is calculated recursively. Furthermore, a sufficient condition is derived to guarantee the stochastic boundedness of the filtering error. Finally, a numerical example is presented to show the effectiveness of the proposed filtering scheme.