New Results on Synchronization of Fractional-Order Memristor‐Based Neural Networks via State Feedback Control

Xiaofan Li,Huiyuan Li,Hongjian Liu,Yuan Ge,Jian-An Fang

doi:10.1155/2020/2470972

Abstract

This paper addresses the synchronization issue for the drive-response fractional-order memristor‐based neural networks (FOMNNs) via state feedback control. To achieve the synchronization for considered drive-response FOMNNs, two feedback controllers are introduced. Then, by adopting nonsmooth analysis, fractional Lyapunov’s direct method, Young inequality, and fractional-order differential inclusions, several algebraic sufficient criteria are obtained for guaranteeing the synchronization of the drive-response FOMNNs. Lastly, for illustrating the effectiveness of the obtained theoretical results, an example is given.

Highlights

In recent years, fractional calculus has become a useful tool in the analysis of slow relaxation phenomena
Inspired by the discussions given above, this paper studies the synchronization issue for fractional-order memristor-based neural networks (FOMNNs) via feedback control
To achieve the synchronization for considered drive-response FOMNNs, two feedback controllers are introduced. en, by adopting nonsmooth analysis, fractional Lyapunov’s direct method and Young inequality, and fractional-order differential inclusions, several algebraic sufficient criteria are obtained for guaranteeing the synchronization for the drive-response FOMNNs

Summary

Introduction

Fractional calculus has become a useful tool in the analysis of slow relaxation phenomena. Dynamic behaviors of fractional-order systems have attracted the attention of many researchers because of their practical applications. Fractional derivative has been introduced to NNs, and dynamic analysis of fractional-order neural networks (FONNs) has become a focus of research and many results have been obtained [24, 25]. Among these dynamic behaviors, as a significant dynamic characteristic, synchronization was firstly introduced [26]. En, by adopting nonsmooth analysis, fractional Lyapunov’s direct method and Young inequality, and fractional-order differential inclusions, several algebraic sufficient criteria are obtained for guaranteeing the synchronization for the drive-response FOMNNs. 2.

Main Results

Numerical Simulation

Conclusions