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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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This paper proposes an adaptive control method based on the feedback linearization technique and a proposed neural network,  for tracking and position control of an industrial manipulator. At first, it is assumed that the dynamics of the system are known and the control signal is constructed  by the feedback linearization method. Then to eliminate the effects of the uncertainties and external disturbances, the parameters of the proposed neural network are learned based on the Lyapunov method such that the sliding condition to be satisfied. The performance of the proposed method is compared with the sliding mode technique in presence of external disturbance, delay and uncertainties. The simulation results verify that the proposed method is effective and can be used in many applications.