Robust Output Synchronization of Arrays of Chaotic Sprott Circuits

Ernesto V Gonzalez Solis,David I Rosas Almeida

doi:10.1155/2017/5201634

Ernesto V Gonzalez Solis, David I Rosas Almeida

Open Access

https://doi.org/10.1155/2017/5201634

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Abstract

This article presents a technique for synchronizing arrays of a class of chaotic systems known as Sprott circuits. This technique can be applied to different topologies and is robust to parametric uncertainties caused by tolerances in the electronic components. The design of coupling signals is based on the definition of a set of functionals which depend on the errors between the outputs of the nodes and the errors between the output of a reference system and the outputs of the nodes. When there are no parametric uncertainties, we establish a criterion to design the coupling signals using only one state variable of each system. When the parametric uncertainties are present, we add a robust observer and a low pass filter to estimate the perturbation terms, which are subsequently compensated through the coupling signals, resulting in a robust closed loop system. The performance of the synchronization technique is illustrated by real-time simulations.

Highlights

Synchronization is a dynamical behavior that two or more systems exhibit when a correlated motion between them is established [1]
This article presents a technique for synchronizing arrays of a class of chaotic systems known as Sprott circuits
We present a technique, based on [16], for synchronizing arrays of a class of chaotic systems known as Sprott circuits

Summary

Introduction

Synchronization is a dynamical behavior that two or more systems exhibit when a correlated motion between them is established [1]. An important characteristic in this work is that the slave system incorporates two control inputs These are designed based on variable structure control and depend on all of states of the systems. The design of the coupling signals is based on a robust discontinuous controller and on an exact deriver that estimates the velocity of each node This is an interesting proposal but it is not applicable to Sprott circuits. We present a technique, based on [16], for synchronizing arrays of a class of chaotic systems known as Sprott circuits. This technique can be applied to different topologies and is robust to parametric uncertainties caused by tolerances in the electronic components.

Preliminary Definitions and Problem Statement

Design of the Coupling Signals

Synchronization Technique Performance

Conclusions