An output feedback tracking controller is proposed for single-input, single-output non-linear systems that are diffeomorphic to the non-linear observer form. Difficulty in obtaining the output injection terms of the non-linear observer form is solved by a numerical technique and the interpolation method using the radial basis function (RBF) network. The trained RBF networks approximate output injection terms in a compact interval and are utilized for building a non-linear observer. In constructing the output tracking controller the backstepping control method is adopted based on the state estimates.