Data-Driven Feedback Linearization with Complete Dictionaries

We consider the feedback linearization problem, and contribute with a new method that can learn the linearizing controller from a library (a dictionary) of candidate functions. When the dynamics of the system are known, the method boils down to solving a set of linear equations. Remarkably, the same idea extends to the case in which the dynamics of the system are unknown and a linearizing controller must be found using experimental data. In particular, we derive a simple condition (checkable from data) to assess when the linearization property holds over the entire state space of interest and not just on the dataset used to determine the solution. We also discuss important research directions on this topic.