Feedback linearization through the lens of data

TL;DR

This paper introduces a data-driven feedback linearization method for unknown nonlinear systems, using a simple algebraic approach to learn the transformation and controller from data, ensuring validity over the entire state space.

Contribution

It proposes a novel algebraic method to perform feedback linearization from data, applicable to unknown systems, and guarantees global validity beyond the training data.

Findings

Method successfully learns linearizing controllers from data.

Solution is valid over the entire state space, not just the dataset.

Approach is simple and algebraic, relying on null space computation.

Abstract

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.