Sampling-Based Event-Triggered Control for Neutral-Type Complex-Valued Neural Networks with Partly Unknown Markov Jump and Time-Varying Delay

Zhen Wang,Yingying Liu,Haiyang Zhang,Lianglin Xiong,Rui Wang

doi:10.1155/2021/5563888

Abstract

This work is devoted to studying the stochastic stabilization of a class of neutral-type complex-valued neural networks (CVNNs) with partly unknown Markov jump. Firstly, in order to reduce the conservation of our stability conditions, two integral inequalities are generalized to the complex-valued domain. Secondly, a state-feedback controller is designed to investigate the stability of the neutral-type CVNNs withH∞performance, making the stability problem a further extension, and then, the stabilization of the CVNNs withH∞performance is investigated through a sampling-based event-triggered (SBET) control for the first time that the transmission event is not triggered except when it violates the event-triggered condition. Finally, two examples are given to illustrate the validity and correctness of our obtained theorems.

Highlights

In terms of the wide application in electromagnetic processing, light wave and sound wave, the neural networks have attracted much attention in recent decades [1,2,3]
Complex-valued signals occur inevitably in practice, and more and more scholars began to make investigations on complex-valued neural networks (CVNNs) [4,5,6,7,8,9,10,11,12]. ere are two methods usually used in the study of CVNNs: one is to divide the neural networks into the real part and imaginary part, the original CVNNs will be changed into real-valued neural networks [8,9,10]. e other method is when the activation function in CVNNs cannot be separated, the stability condition of the system will be sure by the complex-valued LKFs under the condition that the activation function satisfies the complex-valued Lipschitz continuity [11, 12], and it would increase the difficulty of the analysis
According to the state of the art, the LKFs method is often used to deal with neural networks problems because of its simplicity and effectiveness [10, 13,14,15], so it is necessary to construct LKFs with conjugate transpose of state vector to study the CVNNs by the method which do not separate the original system

Summary

Introduction

In terms of the wide application in electromagnetic processing, light wave and sound wave, the neural networks have attracted much attention in recent decades [1,2,3]. Reference [16] was concerned with the stabilization problem for uncertain T-S fuzzy systems with time-varying delays via a robust H∞ state-feedback controller. E. Complexity state-feedback H∞ control problem of time-delay systems is studied in [13], and the reciprocal convex inequality was used to obtain stability conditions of the system. Ere is an output-feedback H∞ control under the event-triggered framework with nonuniform sampling used to explain the stability of networked control systems by Peng and Zheng [33]. A H∞ state-feedback control is proposed to explain the stability of neutral-type CVNNs; to our knowledge, there is little research about the stabilization of neural networks in the complex field. It is the first time to study CVNNs with a sampling-based event-triggered mechanism while avoid splitting the system into two parts, which reduces the computational complexity greatly. A > 0 (or A < 0) means that A is a positive Hermitian matrix (or negative Hermitian matrix), sym{A} AH + A, where AH and AT, respectively, mean the conjugate transpose matrix and transpose matrix of A, ∗ in a matrix denotes the selfconjugate part of the Hermitian matrix

Problem Description and Preliminaries

Main Result

Conclusions