  Controlling nonlinear systems, especially when data are being used to offset
uncertainties in the model, is hard. A natural approach when dealing with the
challenges of nonlinear control is to reduce the system to a linear one via
change of coordinates and feedback, an approach commonly known as feedback
linearization. Here we consider the feedback linearization problem of an
unknown system when the solution must be found using experimental data. We
propose a new method that learns the change of coordinates and the linearizing
controller from a library (a dictionary) of candidate functions with a simple
algebraic procedure - the computation of the null space of a data-dependent
matrix. Remarkably, we show that the solution is valid over the entire state
space of interest and not just on the dataset used to determine the solution.
