This paper presents an adaptive output-feedback control method based on neural networks for flexible link manipulator which is a nonlinear nonminimum phase system. The proposed controller comprises a linear, a neuro-adaptive, and an adaptive robustifying parts. The neural network is designed to approximate the matched uncertainty of the system. The inputs of the neural network are the tapped delays of the system input–output signals. In addition, an appropriate reference signal is proposed to compensate the unmatched uncertainty inherent in the internal system dynamics. The adaptation laws for the neural network weights and adaptive gains are obtained using the Lyapunov’s direct method. These adaptation laws employ a linear observer of system dynamics that is realizable. The ultimate boundedness of the error signals are analytically shown using Lyapunov's method.

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