Stabilization of a chaotic system using indirect adaptive fuzzy control

In this paper, a parameter estimator is developed for the chaotic model whose structure is represented by the Takagi Sugeno model. Using the Takagi Sugeno model of chaotic systems, an adaptive control algorithm is developed based on some conventional adaptive control techniques. Unlike the traditional method, a simpler controller is proposed via fuzzy logic design. Controllers in traditional method are designed based on Lyapunov direct method and are always complicated or the functions of errors. The essential idea behind the on-line estimation of the system is the comparison of the measured state with the state of an estimated model whose structure is the same as that of the parameterized model. Based on the parameter estimation scheme, an indirect adaptive fuzzy controller is designed. The simulation result for the Lorenz system is presented to illustrate the effectiveness of the method in comparison with conventional PDC and adaptive fuzzy feedback linearization method.