Using identical system synchronization with fractional adaptation law for identi cation of a hyper-chaotic system

Synchronization of two chaotic systems has been used in secure communications. In this paper, synchronization of two identical 4D Lu hyper-chaotic systems is used to identify the drive system. Parameters in both drive and response systems are unknown and the systems are synchronized by applying one state feedback controller. Since the goal here is to identify the parameters of the drive system, an adaptive method is used. The stability of the closed-loop system with the controller and convergence of parameters is studied using the Lyapunov theorem. In order to improve the speed of convergence in one parameter, a fractional adaptation law is used and the stability with the fractional law is shown. Finally, the results of both integer and fractional methods are compared.