Abstract

This paper has presented chaos synchronization in the Duffing system using the backstepping approach. Backstepping approach consists of parameters which accept positive values. The parameters are usually chosen optional. The system responses are differently 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. 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.