Synchronization of A Novel 4-D Hyperchaotic Rikitake Dynamo System Along With Unknown Parameters Via Adaptive Integral Sliding Mode

Abstract

In this paper, a new approach is proposed for synchronization of 4-D identical hyperchaotic Rikitake dynamo system, along with unknown and known parameters via adaptive integral sliding mode control. Second and the major contribution of this article is the reduction of controllers of slave system from 4 to 3 (required for the tracking of the output of master / drive system). Firstly, the error system is transformed into a special structure containing nominal part and some unknown terms. Later 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. Effectualness of the proposed strategy in coupling with the kinetics of the systems is confirmed by the simulation results.