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This paper proposes direct adaptive fuzzy control with less restriction on control gain for siso nonlinear systems and is presented a simplified type-2 fuzzy system. Adaptation law is derived based on Lyapunuv stability analysis that assures adaptive parameters and tracking error to be bonded. Since in addition to consequent parameters,width and centers of the membership functions are tuned then the estimation error is very small so as to be negligible.Furthermore, the number of membership functions required is seen to be less than that needed with type-1 fuzzy sets. The simulation results that are conducted on inverted pendulum and magnetic levitation systems confirm the efficacy of the proposed scheme. In the presence of noise the reference input is tracked very well and tracking error is very small.

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In this study a model reference rough-radial basis function neural network controller with feedback error learning for control of a class of nonlinear systems subject to unknown bounded uncertainty is proposed. The proposed controller in hybrid form includes the classic controller and rough- radial basis function neural network controller. Because of using the classic controller with the neural network controller, it is expected that the transient response is bounded. The weights of the output layer of the neural network controller are interval variables. Using an appropriate Lyapunov function, stable adaptation laws for these weights according to the output of the classic controller and based on stability are derived. To show the efficacy of the proposed controller, results of simulation that is applied to Duffing Oscillator and Genesio- Tesi are shown and results are compared with the results when simple model reference radial basis function neural network is used as the controller. The results show that the proposed method is more robust against uncertainty when it is compared to model reference radial basis function neural network controller. Also, using the proposed controller, synchronization of chaotic systems is performed. The results verified the effectiveness of the proposed controller.