Stabilization of feedback linearizable systems using a radial basis function network

The main obstacle in the practical use of the feedback linearization is the difficulty in obtaining a linearizing feedback and a coordinate transformation map. Finding a desired transformation map and feedback turns out to be finding an integrating factor for an annihilating one-form. In this work, we develop numerical algorithms for an integrating factor and the corresponding zero-form. Employing a radial basis function (RBF) neural network as an interpolation method for the data resulted from the numerical algorithms, the authors obtained an approximate integrating factor and zero-form in closed forms. Finally, they construct a stabilizing controller based on a linearized system with the use of the approximate integrating factor and zero-form.