Abstract
Synchronization is very useful in many science and engineering areas. In practical application, it is general that there are unknown parameters, uncertain terms, and bounded external disturbances in the response system. In this paper, an adaptive sliding mode controller is proposed to realize the projective synchronization of two different dynamical systems with fully unknown parameters, uncertain terms, and bounded external disturbances. Based on the Lyapunov stability theory, it is proven that the proposed control scheme can make two different systems (driving system and response system) be globally asymptotically synchronized. The adaptive global projective synchronization of the Lorenz system and the Lü system is taken as an illustrative example to show the effectiveness of this proposed control method.
Highlights
The cooperative behavior of coupled nonlinear oscillators is of interest in connection with a wide variety of different phenomena in physics, engineering, biology, and economics
Synchronization occurs when oscillatory systems via some kind of interaction adjust their behaviors relative to one another so as to attain a state where they work in unison [1], since the individual oscillators display chaotic dynamics in many cases and it is very important to analyze the synchronization of chaotic systems
This paper mainly focuses on the projective synchronization of nonidentical structure chaotic systems with fully unknown parameters, uncertain terms, and external bounded disturbances
Summary
The cooperative behavior of coupled nonlinear oscillators is of interest in connection with a wide variety of different phenomena in physics, engineering, biology, and economics. To achieve projective synchronization of identical or nonidentical chaotic systems with different initial conditions, many effective control methods have been proposed, such as linear and nonlinear feedback control [26], adaptive control [27], impulsive control [28], and sliding mode control [29] With these control schemes, many dynamical systems, such as the Lorenz system, the Chen system, the Rossler system, and some other chaotic or hyperchaotic systems [30, 31], with known or unknown parameters, are all synchronized by various control methods based on Lyapunov stability theory. It is desirable to achieve the projective synchronization of nonidentical chaotic systems with unknown parameters, uncertain terms, and bounded external disturbances via adaptive sliding mode controller. Synchronization analysis of the Lorenz system and the Lusystem is given in Section 4, and Sections 5 and 6 provide the numerical simulations and concluding remarks of this study, respectively
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
