Abstract—In this paper, first known chaotic system, Chen equation, was selected as chaotic system. One of the best control methods that would be used for stabilization this systems, was Backstepping. In this paper this method is improved to Generalized Backstepping Method (GBM). For this new method, expose a new theorem and its proof and for showing its abilities, control Chen equation. Generalized Backstepping approach consists of parameters which accept positive values. The system responded differently for each value. Genetic algorithm can select appropriate and optimal values for the parameters. GA by minimizing the fitness function can find the optimal values for the parameters. Fitness function forces the system error to decay to zero rapidly that it causes the system to have a short and optimal setting time. Fitness function also makes an optimal controller and causes overshoot to reach to its minimum value. This hybrid makes an optimal backstepping controller.
Index Terms—Chen chaos, lyapunov, generalized backstepping method, ANFIS.
A. R. Sahab is with the Islamic Azad University Lahijan Branch, Lahijan, Guilan, Iran (e-mail: email@example.com).
M. Taleb Ziabari is with the Islamic Azad University Qazvin Branch, Qazvin, Iran (e-mail: firstname.lastname@example.org)
Cite: A. R. Sahab and M. Taleb Ziabari, "Generalized Backstepping Method Based Control Chen Chaotic System Using Adaptive Neuro-Fuzzy Inference System," International Journal of Information and Electronics Engineering vol. 2, no. 5, pp. 667-671, 2012.