Output feedback direct adaptive neural network control for uncertain SISO nonlinear systems using a fuzzy estimator of the control error

A direct adaptive control algorithm, based on neural networks (NN) is presented for a class of single input single output (SISO) nonlinear systems. The proposed controller is implemented without a priori knowledge of the nonlinear systems; and only the output of the system is considered available for measurement. Contrary to the approaches available in the literature, in the proposed controller, the updating signal used in the adaptive laws is an estimate of the control error, which is directly related to the NN weights instead of the tracking error. A fuzzy inference system (FIS) is introduced to get an estimate of the control error. Without any additional control term to the NN adaptive controller, all the signals involved in the closed loop are proven to be exponentially bounded and hence the stability of the system. Simulation results demonstrate the effectiveness of the proposed approach.