Synchronization and Antisynchronization Between Two Non-Identical Chua Oscillators via Sliding Mode Control

This paper presents the synchronization and antisynchronization scheme between the Chua and modified Chua oscillators. Two cases are considered based on systems known and unknown parameters. In case of known parameters, synchronization and antisynchronization are achieved via sliding mode control, while in case of unknown parameters, adaptive integral sliding mode control is applied. To employ the adaptive integral sliding mode control, the error system is transformed into a special structure containing nominal part and some unknown terms. The unknown terms are computed adaptively. Then, the error system is stabilized using integral sliding mode control. The stabilizing controller for the error system is constructed, which consists of the nominal control plus some compensator control. To avoid the chattering phenomenon, smooth continuous compensator control is used instead of traditional discontinuous control. The compensator controller and the adapted law are derived in such a way that the time derivative of a Lyapunov function becomes strictly negative. Numerical results are shown to illustrate and validate the synchronization schemes presented in this paper.