A study on integral control for synchronization of chaotic systems

Abstract

In this thesis, we propose the integral control for the synchronization of different chaotic systems with unknown dynamics.First, the synchronization of two different chaotic systems with unknown dynamics is discussed. We proposed a high gain integral controller for synchronization of unknown drive and response system. The proposed integral controller utilizes the error signal so that the resulting error dynamical system is converted into a singular perturbation form. Perturbation theory is ised to demonstrate that the synchronization error of the resulting feedback systemconverges to zero.Second, an integral control scheme for interconnected unknown chaotic systems is addressed. Considering one network as the drive node and the others as the response nodes, the drive-response system achieves synchronousstates through a suitably designed integral controller. The error dynamics of the resulting feedback system can be considered as a two-time-scale nonlinear dynamic system which has fast and slow dynamics. The sufficient condition for stability of two-time-scale nonlinear dynamic systems was derived using Tikhonov’s theorem. The proposed controller guarantees convergence of thesynchronization error to zero.