Distributed l 2 − l ∞ filtering over wireless sensors based on adaptive event triggering

Abstract

This paper investigates the design problem of a set of distributed filters. These adaptive event-triggered (AET) filters have the $l_2-l_{\infty }$ property and are suitable for sensor networks characterized by random measurement data loss and dynamic topology switching. In a distributed filtering network, each local filter estimates the system’s state not only relying on the node’s individual information but also using information from neighboring nodes in the network topology. The adaptive event triggering condition is determined by the combination of the latest release data of the filter itself, the estimated value of the current moment, and the latest release data of the neighboring nodes. The event triggering mechanism adopts a threshold adaptive adjustment scheme, which dynamically changes the threshold parameter according to the filtering error under the premise of guaranteeing the filter performance, thus maximally saving the network communication resources. Initially, we used a binary sequence to describe the random loss of sensor measurements, and a Markov chain is used to describe the switching of the filtering network topology. Secondly, a Lyapunov function is created to examine the $l_2-l_{\infty }$ performance index of the filtering error system and investigate its mean square exponential stability. Subsequently, the distributed filter is formulated, and its parameters are determined using the linear matrix inequality approach. Ultimately, the validity of the proposed method is substantiated through numerical illustrations.