Inverse optimal control for a new chaotic system

A relatively simple chaotic system and its basic dynamic behaviors are introduced. By applying the Routh-Hurwitz criterion, the problem of the stability of equilibrium points is discussed and some results are obtained. Based on the theory of Lyapunov stability and by the inverse optimal controlling approach, a controller is designed for controlling a new type of chaotic system. The controller is a linear state feedback controller and is very simple. With it the system orbit can be controlled to its originally unstable zero equilibrium point. By numerical simulation the effectiveness of the controller is proved.