Controlling Hyperchaos and Synchronization of an Uncertain Modified Hyperchaotic LU System

Sundarapandian Vaidyanathan

doi:10.5121/ijics.2012.2103

Abstract

This paper investigates the adaptive cont rol and synchronization of anuncertain modified hyperchaotic Lu system recently discovered by Wang, Zhang, Zheng and Li(2006). This paper deploysnonlinear control for controlling the hyperchaos of the modified hyperchaotic Lu system with unknown parameters and then synchronizing two identical modified hyperchaotic Lu systems with unknown parameters.First, adaptive control laws are designed tostabilize the modified hyperchaotic Lu system to its unstable equilibrium at the origin based on the adaptive control theoryand Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identicalmodified hyperchaotic Lu systems with unknown parameters. Numerical simulations are presented to demonstrate theeffectiveness of the proposed adaptive control and synchronization schemes.

Highlights

A chaotic system is a nonlinear dynamical system with the following characteristics: extreme sensitivity to changes in initial conditions, random-like behaviour, deterministic motion, trajectories of chaotic systems pass through any point an infinite number of times
The control of chaotic systems is to design state feedback control laws that stabilizes the chaotic systems around the unstable equilibrium points
The modified hyperchaotic Lü system is described by the dynamics x 1 = a(x2 − x1 + x2 x3 )

Summary

INTRODUCTION

A chaotic system is a nonlinear dynamical system with the following characteristics: extreme sensitivity to changes in initial conditions, random-like behaviour, deterministic motion, trajectories of chaotic systems pass through any point an infinite number of times. The seminal work by Pecora and Carroll (1990) has been followed by a variety of impressive approaches in the literature such as the sampled-data feedback method [11], OGY method [12], time-delay feedback method [13], backstepping method [14], active control method [15,16,17,18,19,20], adaptive control method [21,22,23,24,25], sliding mode control method [26,27,28], etc.

Theoretical Results

Numerical Results

CONCLUSIONS