Synchronization of Hyperchaotic Systems under Active Adaptive Sliding Mode Control

Under the existence of system uncertainties and external disturbances, complete synchronization and anti-synchronization between two identical or different hyperchaotic systems are investigated in the paper. Firstly, an active control is used to eliminate the nonlinear part of the error. Then the sliding mode controller is designed based on suitable sliding surface. After that the adaptive updating law is designed to estate the bound of the uncertainties and external disturbances under the combination of active sliding mode control and adaptive control. The structure of the master and slave hyperchaotic systems has no restrictive assumption about the bound of the uncertainties and external. The active adaptive sliding mode controller (AASMC) is proposed to drive the state of slaver system trajectories into or opposites to the state of master system. The active adaptive sliding mode controller is proposed to realize synchronization and anti-synchronization by changing the parameter in the control function respectively. Moreover, a strict proof of the stability of the error dynamics is derived based on the Lyapunov stability theory. Finally, the corresponding numerical simulations are demonstrated the robustness and efficiency of the proposed controller.