Identification of 4D Lü hyper-chaotic system using identical systems synchronization and fractional adaptation law

In this paper, the parameters of a 4D Lü hyper-chaotic system are identified via synchronization of two identical systems. Unknown parameters of the drive system are identified by an adaptive method. Stability of the closed-loop system with one state feedback controller is studied by using the Lyapunov theorem. Also the convergence of the parameters to their true values is proved. Then a fractional adaptation law is applied to reduce the time of parameter convergence. Finally the results of both integer and fractional methods are compared.