Synchronization of Genesio chaotic system via backstepping approach

Backstepping design is proposed for synchronization of Genesio chaotic system. Firstly, the control problem for the chaos synchronization of nominal Genesio systems without unknown parameters is considered. Next, an adaptive backstepping control law is derived to make the error signals between drive Genesio system and response Genesio system with an uncertain parameter asymptotically synchronized. Finally, the approach is extended to the synchronization problem for the system with three unknown parameters. The stability analysis in this article is proved by using a well-known Lyapunov stability theorem. Note that the approach provided here needs only a single controller to realize the synchronization. Two numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.