Adaptive control and synchronization of an uncertain new hyperchaotic Lorenz system

Abstract

This paper is involved with the adaptive control and synchronization problems for an uncertain new hyperchaotic Lorenz system. Based on the Lyapunov stability theory, the adaptive control law is derived such that the trajectory of hyperchaotic Lorenz system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. Furthermore, an adaptive control approach is presented to the synchronizations between two identical hyperchaotic systems, particularly between two different uncertain hyperchaotic systems. Numerical simulations show the effectiveness of the presented method.

Backstepping Projectivesynchronization Scheme Andadaptive Function Projectivesynchronization Scheme Onchaotic Dumbell Satellitemodel : A Comparative Study

“…fig 1 and 2 imply that we are successful in achieving PS between (2) and (3). Now, to observe the achievement of FPS,we note that figures 10 to 14 show the time evolution of the uncertain parameters a 1 , b 1 , c 1 , d 1 , f 1 of the slave system and we find that…”

“…Ever since the drive-response method for synchronization of two identical chaotic systems with different initial conditions (Pecora & Carroll, 1990) was proposed, Chaos Synchronization has become an active research subject in non-linear science and it has been intensively studied in the last two decades (Hu & Zhang, 2008;Cai et al, 2008;Elabbasy et al, 2006). Various types of chaos synchronization have been proposed such as Complete Synchronization (Kuntanapreeda, 2009), Phase Synchronization (Erjaee & Momani, 2008), Generalized Projective Synchronization (Farivar et al, 2009), Anti-Synchronization (El-Dessoky, 2010), Lag Synchronization (Shahverdiev & Sivaprakasam, 2002), Modified Projective Synchronization (Li, 2007) and Function Projective Synchronization (Du, 2010;Luo & Wei, 2009).…”

Adaptive Synchronization for Hyperchaotic Liu System

“…A hyperchaotic system is a chaotic system with at least two positive Lyapunov exponents which improves the security by generating more complex dynamics and so hyperchaotic systems have much more applications than low-dimension chaotic systems in the areas such as secure communication and image encryption, etc. Therefore in the past three decades, an increasing interest has been devoted to the study of chaos synchronization for hyperchaotic systems and plenty of research works can be found in literature [13,[19][20][21][22][23][24][25]. However, there are few studies about the adaptive synchronization of hyperchaotic Liu system that was introduced in [26].…”