Stabilizing a Class of Chaotic Systems by Using Adaptive Feedback Control

In this paper, an adaptive feedback control method is presented to stabilize a class of chaotic systems, the structural function of whose is not necessarily to satisfy the Lipsichtz conditions, but bounded by a polynomial of the infinity norm of the system state with the gains unknown. The adaptive feedback controller uses a simple polynomial function of the system state, moreover only one component in each dimension. To check the theoretical results, we try to stabilize the Lorenz system on numerical simulations. This paper generalizes the Huang's result [Phys. Rev. Lett. 93(2004) 214101-1].