Abstract
In this article, first famous chaotic system, Chua equation, was choiced as chaotic system. One of the best control methods that would be used for stabilization this systems, was Backstepping. In this article this technique is improved to Generalized Backstepping Method (GBM). For this new method, exhibit a new theorem and its proof and for showing its abilities, control Chua equation. Generalized Backstepping approach consists of parameters which accept positive values. The system replied differently for each value. Genetic algorithm can select suitable 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.
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