Finite-Time Distributed $H_{\infty }$ Filtering in Sensor Networks With Switching Topology and Two-Channel Stochastic Attacks

Abstract

This paper investigates the finite-time distributed $H_{\infty }$ filtering problem in sensor networks with switching topology and two-channel stochastic attacks. The two-channel stochastic deception attacks are introduced, encompassing network attacks in the communication channel between the model and the sensor, as well as in the channel between the sensors, implemented through an independent Bernoulli process with uncertain probabilities. To address this problem, a novel distributed filter with two-channel stochastic attacks is designed, considering the switching topology and information transmission between sensors. The corresponding filtering error system is proposed. By utilizing the Lyapunov function technique and stochastic analysis method, some new sufficient conditions are established to demonstrate the stochastic finite-time boundability of the filtering error system and ensure satisfaction of the $H_{\infty }$ performance index. Moreover, the optimal $H_{\infty }$ performance index problem is solved to determine the distributed filter gains and establish the lower boundness of the average dwell time of the topology switching signals. Finally, the effectiveness of the proposed design method is validated through two simulation examples.