On modified second-order sliding mode synchronization of two different fractional order Hyperchaotic systems

Abstract

A modified second-order sliding mode (SOSM) control scheme is developed to synchronize two different fractional order hyperchaotic systems. On the basis of chattering free SOSM control scheme, a special fractional sliding mode surface is firstly proposed. Subsequently, a robust control law is designed to ensure the occurrence of sliding mode in a given time. This control scheme is rigorously proved by Lyapunov stability theory. Finally, a numerical example is given to illustrate the effectiveness of the proposed synchronization approach.