Neural-Impulsive Pinning Control for Complex Networks Based on V-Stability

Daniel Ríos-Rivera,Alma Y Alanis,Edgar N Sanchez

doi:10.3390/math8091388

Daniel Ríos-Rivera, Alma Y Alanis + Show 1 more

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https://doi.org/10.3390/math8091388

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Journal: Mathematics	Publication Date: Aug 19, 2020
Citations: 4	License type: CC BY 4.0

Affiliation: University of Guadalajara

Abstract

In this work, a neural impulsive pinning controller for a twenty-node dynamical discrete complex network is presented. The node dynamics of the network are all different types of discrete versions of chaotic attractors of three dimensions. Using the V-stability method, we propose a criterion for selecting nodes to design pinning control, in which only a small fraction of the nodes is locally controlled in order to stabilize the network states at zero. A discrete recurrent high order neural network (RHONN) trained with extended Kalman filter (EKF) is used to identify the dynamics of controlled nodes and synthesize the control law.

Highlights

In recent years, complex networks have been gaining more attention in the scientific community, with a wide range of applications, from computer science to sociology [1]
A technique developed for the control of complex dynamical networks is pinning control, which consists of controlling only a small fraction of nodes of a complex network [3]
Numerous studies have been published around this pinning control technique, of particular interest to this study is the one of V-stability [4], in which the stability problem for a complex network with different dynamics in its nodes is transformed to verify positive definiteness of an associated matrix

Summary

Introduction

Complex networks have been gaining more attention in the scientific community, with a wide range of applications, from computer science to sociology [1]. There are many techniques in control theory that have been developed over the years in order to achieve stability around a given equilibrium point [2]. Using a particular method of control depends on the designer or the type of system that is being worked on. A technique developed for the control of complex dynamical networks is pinning control, which consists of controlling only a small fraction of nodes of a complex network [3]. Numerous studies have been published around this pinning control technique, of particular interest to this study is the one of V-stability [4], in which the stability problem for a complex network with different dynamics in its nodes is transformed to verify positive definiteness of an associated matrix

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