In this paper an adaptive tracking control algorithm and its step by step implementation procedure are developed for a class of nonlinear plants within a U-model framework with unknown parameters. With the author’s previous justification, not only the control oriented model represents a wide range of smooth (polynomial) nonlinear dynamic plants (without using linearisation approximation at all), but also make almost all linear control system design techniques directly applicable (with a root solver bridging the linear design and calculation of controller output). A new technique is proposed to design an online control algorithm using the Radial Basis Functions Neural Network (RBFNN). The plant parameters are estimated online and are used to update the weights of the RBFNN. The weights update equations are derived based on the well known LMS (least mean square). A number of simulated case studies are conducted to illustrate the efficiency of the claimed insight and design procedure.