Anti-synchronizing Backstepping Control Design for Arneodo Chaotic System

In this paper, we derive new results for backstepping controller design for the anti-synchronization of Arneodo chaotic system (1980). Backstepping control is a recursive procedure that combines the choice of a Lyapunov function with the design of a feedback controller. In anti-synchronization of chaotic systems, the states of the synchronized systems have the same absolute values, but opposite signs. First, we derive an active backstepping controller for the anti-synchronization of identical Arneodo chaotic systems. Next, we derive an adaptive backstepping controller for the anti-synchronization of identical Arneodo chaotic system, when the system parameters are unknown. The anti-synchronization results for Arneodo chaotic systems have been proved using Lyapunov stability theory. Numerical simulations have been shown to illustrate the backstepping controllers derived in this paper for Arneodo chaotic system.