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.

I. Introduction

Sensor networks usually consist of the majority of geographically distributed sensor nodes that work together to collaboratively collect, manage and process the data or events of interest, which have been found a wide-scope domain of application in nowadays military facilities, power grids and manufacturing automation, etc., see e.g. [1], [2], [26]. As a critical research topic in sensor networks, distributed has attracted considerable attention during the past decades because of its prominent theoretical importance and engineering insights [3]–[5]. Compared with the traditional single sensor filtering algorithm [6], [7], [10], [11], [28], [29], the key feature of the distributed filtering over sensor networks is that available information on a single sensor node comes both from its own measurements and its adjacent sensors through information exchange. Due to collaborative information processing, the distributed filtering approach is of robustness against the sensor unreliability, which is thus believed to have a better filtering performance.