SYNCHRONIZATION AND ANTISYNCHRONIZATION OF CHAOTIC SYSTEMS USING ADAPTIVE INTEGRAL SLIDING MODE

Abstract

This thesis presents new control strategy based on Sliding Mode and Adaptive Integral Sliding Mode for the synchronization and anti-synchronization of chaotic systems. Two cases are considered: (i) systems with known parameters, and (ii) systems with unknown parameters. In case (i) the synchronization and antisynchronization are achieved through sliding mode control, while in case (ii) the adaptive integral sliding mode control is used. 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. The compensator controller and the adapted laws are derived on the basis of Lyapunov stability theory. Three numerical examples, (i) Lorenz system (ii) hyper-chaotic Lorenz-Stenflo system and (iii) hyper-chaotic memristor oscillator systems are shown to illustrate and validate the synchronization schemes presented in this thesis.