Controlling Chen's chaotic attractor using two different techniques based on parameter identification

In this letter, the observer technique is applied to the identification of the unknown parameter of Chen's chaotic system. Based on this observer, an efficient backstepping design and a simple controller are developed for controlling Chen's chaotic system. Both of them avoid including divergence factor as in Ref. [Lu JH, Zhang S. Controlling Chens chaotic attractor using backstepping design based on parameter identification. Phys Lett A 2001;286:148]. Especially in the latter scheme, a simple controller is designed via extending equilibrium manifolds of the origin system, which can stabilize the chaotic irregular states not only to arbitrary desired equilibrium-alike point but also to any target periodic orbits as designated online. Numerical simulation is provided to show the effectiveness of the proposed control method.