Synchronization control of cross-strict feedback hyperchaotic system based on cross active backstepping design

This Letter presents a novel cross active backstepping design method for synchronization control of cross-strict feedback hyperchaotic system, in which the ordinary backstepping design is unavailable. The proposed control method, combining backstepping design and active control approach, extends the application of backstepping technique in chaos control. Based on this method, different combinations of controllers can be designed to meet the needs of different applications. The proposed method is applied to achieve chaos synchronization of two identical cross-strict feedback hyperchaotic systems. Also it is used to implement synchronization between cross-strict feedback hyperchaotic system and Rössler hyperchaotic system. Numerical examples illustrate the validity of the control method.