%0 Journal Article
%T Control and Synchronization of Chaotic and Hyperchaotic Lorenz Systems via Extended Backstepping Techniques
%A O. S. Onma
%A O. I. Olusola
%A A. N. Njah
%J Journal of Nonlinear Dynamics
%D 2014
%R 10.1155/2014/861727
%X We propose novel controllers for stabilization and tracking of chaotic and hyperchaotic Lorenz systems using extended backstepping techniques. Based on the proposed approach, generalized weighted controllers were designed to control chaotic behaviour as well as to achieve synchronization in chaotic and hyperchaotic Lorenz systems. The effectiveness and feasibility of the proposed weighted controllers were verified numerically and showed their robustness against noise. 1. Introduction Chaos theory has found application in many areas of studies; these include mathematics, physics, biology, engineering, economics, and politics [1¨C3]. One of the most successful applications of chaos theory has been in ecology, where dynamical systems have been used to show how population growth under density dependence can lead to chaotic dynamics. Chaos theory is also currently being applied to medical studies of epilepsy, specifically to the prediction of seemingly random seizures by observing initial conditions [4]. Furthermore, a related field of physics called quantum chaos theory investigates the relationship between chaos and quantum mechanics [5]. In addition, another field called relativistic chaos [6] has emerged to describe systems that follow the laws of general relativity. Chaotic phenomenon could be beneficial in some applications; however, it is undesirable in many engineering and other physical applications and should therefore be controlled in order to improve the system performance. Chaos control is concerned with using some designed control inputs to modify the characteristics of a parameterized nonlinear system so that the system becomes stable at a chosen position or tracks a desired trajectory [7]. Several techniques have been deviced for chaos control but mostly are for development of two basic approaches: the OGY (Ott, Grebogi, and Yorke) method and Pyragas continuous control. Both methods require a previous determination of the unstable periodic orbits of the chaotic system before the controlling algorithm can be designed. Experimental control of chaos by one or both of these methods has been achieved in a variety of systems, including turbulent fluids, oscillating chemical reactions, magneto-mechanical oscillators, and cardiac tissues [8]. Since the idea of synchronization of chaotic systems was proposed by Pecora and Carroll in 1990, [9], chaos synchronization has received an increasing attention due to its theoretical challenge and its potential applications in secure communications, chemical reactions, biological systems, information science,
%U http://www.hindawi.com/journals/jndy/2014/861727/