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A new Gaussian radial basis function static neurocontroller is presented for stable adaptive tracking control. This is a two-stage controller acting in a supervisory fashion by means of a switch logic and allowing arbitration between a neural network (NN) and a robust proportional-derivative controller. The structure is intended to reduce the effects of the curse of dimensionality in multidimensional systems by fully exploiting the mechanical properties of the robot manipulator. A new factorization of the Coriolis/centripetal matrix is used, leading to an NN model that is much smaller than the dynamic ones. By resorting to the extended multivariate Shannon theorem and the computation of the effective bandwidth of the revolute robot manipulators, the network parameters are tuned. Stability and convergence properties are analyzed. This provides the assurance of reliability and effectiveness to make such controller viable. A robot manipulator with two degrees of freedom is employed to study the adaptive features of the neural control algorithm. Finally, the effectiveness of the proposed method is compared to the nonadaptive case.