Sliding mode control of a hyper-chaos system with only one nonlinear term

A four-dimensional dynamic system with only one nonlinear term was constructed and analysed the chaotic complex dynamic characteristics, including the space trajectory, the Lyapunov exponent and the Poincare map. These characteristics enable us to know deeply them, and indicate that the four-dimensional dynamical system contains hyper-chaotic attractor. For overcoming the shortcomings that the system can never be controlled to target orbit precisely in feedback control theory, the chaotic orbits were stabilized to arbitrary chosen any fixed points and any periodic orbits by means of sliding mode method, and MATLAB Simulations were presented to confirm the validity of the controller. The results show that using sliding mode method can make the system track target orbit smoothly with short transition time.