Event-Triggered    H   ∞    Filtering for Markovian Jump Neural Networks under Random Missing Measurements and Deception Attacks

Jinxia Wang,Miao Ma,Jinfeng Gao,Tian Tan,Jiaqi Wang,Sergey Dashkovskiy

doi:10.1155/2020/4151542

Abstract

This paper concentrates on the event-triggered H ∞ filter design for the discrete-time Markovian jump neural networks under random missing measurements and cyber attacks. Considering that the controlled system and the filtering can exchange information over a shared communication network which is vulnerable to the cyber attacks and has limited bandwidth, the event-triggered mechanism is proposed to relieve the communication burden of data transmission. A variable conforming to Bernoulli distribution is exploited to describe the stochastic phenomenon since the missing measurements occur with random probability. Furthermore, seeing that the communication networks are vulnerable to external malicious attacks, the transferred information via the shared communication network may be changed by the injected false information from the attackers. Based on the above consideration, sufficient conditions for the filtering error system to maintain asymptotically stable are provided with predefined H ∞ performance. In the end, three numerical examples are given to verify the proposed theoretical results.

Highlights

Neural networks (NNs) have been attached increasing importance by many researchers on account of the wide applications in robotization, deep learning, optimization problem, and pattern recognition in recent decades
By using the universal approximation ability of NNs, an adaptive dynamic surface control method is provided for the nonlinear systems [3, 4]
In practical application, NNs face many challenges, such as information interruption, random interference, and variations of the network environment. ese impulsive effects can be simulated by a Markovian jump chain since the stochastic Markovian jump process can effectively reduce the conservatism

Summary

Introduction

Neural networks (NNs) have been attached increasing importance by many researchers on account of the wide applications in robotization, deep learning, optimization problem, and pattern recognition in recent decades. In [14], Xu et al discuss the design method of nonsynchronous H∞ filter for the singular Markovian jump systems, in which multiple redundant channels are utilized to enhance the quality of data transmission. A secure filter is devised for the delayed stochastic nonlinear systems with a novel multiple-channel attack model [33]. The issue of H∞ filtering for MJNNs under randomly occurring missing measurements and deception attacks is discussed. (2) In the design of filter, randomly occurring missing measurements and cyber attacks are considered to make it closer to the practical communication environment. Notations: in this paper, the superscripts “T” and “−1” represent the transpose and the inverse of a matrix; Rn denotes n-dimensional Euclidean space; Rn×m denotes the set of real matrices with m rows and n columns; P > 0 (P ∈ Rn×m) means that P is a real symmetric positive definite matrix; L2[0, ∞) denotes the space of square-integrable vector functions over [0, ∞); I is a identity matrix; and ∗ represents the symmetric term of a symmetric matrix

Problem Elaboration

Main Results

Numerical Simulation