Adaptive Backstepping Sliding-Mode Synchronization of Uncertain Multi-Scroll Chaotic System

A synchronization method of adaptive backstepping sliding-mode control is presented based on the multiscroll chaotic systems with hysteresis nonlinear function and unknown parameters. The strategy is designed by a step-by-step procedure interlacing. At each step, a coordinate transformation, the design of a virtual control via a Lyapunov technique and the definition of a tuning function are derived, then, the globally control of the system is obtained. As a result, synchronization of the chaotic systems is achieved by controller. The synchronization error system arrives at the sliding-mode in finite time. Then, the controller can drive the error system to reach the origin. The identification of the unknown parameters is obtained at the same time. Because of using the adaptive arithmetic and sliding-mode control, the controller is robustness of parameter uncertainties and disturbances. The analyses and simulation results proved the effectiveness and feasibility of the method.