Abstract
This paper deals with the synchronization of two extended Bonhoffer‐Van der Pol (B‐VDP) oscillators. A Lyapunov‐based controller and a sliding mode controller are proposed for the synchronization of the oscillators. Both design schemes use a single input controller acting on one state only. Asymptotic stability results for the closed‐loop system are derived using Lyapunov theory. It is shown that the proposed controllers effectively synchronize the driver and the response systems for the case when nominal values of the system parameters are used, and for the case when parameter perturbations are introduced. Simulation results are presented to show the effectiveness of the proposed controllers.
Highlights
Chaotic systems represent an interesting class of nonlinear systems
The synchronization phenomenon has been used in several key applications such as network security 2 and biological oscillators 3
Several control strategies were suggested for the synchronization and anti-synchronization of chaotic systems; the suggested strategies include backstepping control, adaptive control, and active control
Summary
Chaotic systems represent an interesting class of nonlinear systems. They are known to be highly sensitive to small changes in the initial conditions 1. In the past two decades, the problem of synchronization and antisynchronization of chaotic systems has attracted a lot of interest. Several control strategies were suggested for the synchronization and anti-synchronization of chaotic systems; the suggested strategies include backstepping control, adaptive control, and active control. An adaptive backstepping control law which is designed to control a class of chaotic systems is given in 5 ; the chaotic system is transformed into a nonautonomous strict feedback form, the developed backstepping controller is applied to asymptotically track a given reference signal. In 6 , an integral sliding mode controller SMC with a dynamic
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