Probabilistic-Constrained Distributed Filtering for a Class of Nonlinear Stochastic Systems Subject to Periodic DoS Attacks

This paper investigates the probabilistic-constrained distributed filtering problem for a class of nonlinear stochastic systems with state constraints and cyber attacks. The considered cyber attacks are periodic denial-of-service (DoS) attacks which are modeled by a kind of periodic pulse-width-modulated (PWM) jamming signals. Different from some existing works, by using the proposed filter design method, the probability of the filtering error exceeding a threshold can be guaranteed below a certain level quantitatively. Furthermore, in order to economize the limited bandwidth resources, an event-triggered communication scheme (ETS) is designed for the data transmission. The aim of the problem addressed is to design a time-varying distributed filters such that: 1) the probability of the filtering error restricted to a given ellipsoid is larger than a specified value; and 2) the obtained ellipsoid threshold is minimized in the sense of matrix norm at each time point. To achieve this purpose, a recursive linear matrix inequality method is utilized and sufficient conditions are derived. Moreover, the filter parameters are explicitly determined in terms of the solution to certain matrix inequalities. Finally, the reliability and applicability of the proposed distributed filtering strategy are demonstrated by an illustrative example.