Feedback Linearization Through the Lens of Data

Controlling nonlinear systems is challenging, especially when data are used to address model uncertainties. By contrast, linear systems are well understood. Thus, a common strategy is to transform the nonlinear system into a linear one through a change of coordinates and feedback-a technique 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.