Stabilization and Tracking in Lorenz Chaotic System using Optimal Generalized Backstepping Method

This study deals with the control chaos using generalized backstepping method. This new method to control nonlinear systems was called generalized backstepping method because of its similarity to backstepping but its abilities to control more systems than backstepping. Generalized backstepping approach consists of parameters which accept positive values. The parameters are usually chosen optional. The system responses are different for each value. It is necessary to select proper parameters to obtain a good response because the improper selection of the parameters lead to inappropriate responses or even may lead to instability of system. 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. This selected fitness function is for minimizing the least square error. 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. Keywords— Lorenz chaos, Lyapunov, Generalized Backstepping Method, Genetic Algorithm.