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).
