Complex Synchronization and Parameter Identification of Nonlinear Complex Chaotic Systems Using Adaptive Integral Sliding Mode Control

Abstract

This thesis presents three different kinds of complex synchronization (CS), (i) Complex Complete Synchronization (CCS), (ii) Complex Projective Synchronization (CPS), (iii) Complex Generalized Synchronization (CGS) of Identical and Nonidentical Nonlinear Complex Systems with unknown parameters. Based on adaptive integral sliding mode control, an adaptive controller and parameter update laws are designed to realize CCS, CPS and CGS. 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 adaptive 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 law are derived in such a way that the time derivative of a Lyapunov function becomes strictly negative. The proposed scheme is successfully applied to complex chaotic nonlinear systems with unknown parameters for the realization of (i) Complex Complete Synchronization (CCS),(ii) Complex Projective Synchronization (CPS),(iii) Complex Generalized synchronization (CGS).