A Koopman-theoretic approach towards Data-driven Feedback Linearization

Feedback Linearization is challenging to implement in practice due to the need for an accurate model of the system. To overcome this challenge, we present a Koopman-theoretic approach to feedback linearization, that complements the data-driven methods that approximate Koopman representations. Specifically, the solution to feedback linearization is shown to admit a spectral decomposition in terms of Koopman eigenfunctions and eigenvalues. This results in the development of sufficient conditions under which an exact solution to feedback linearization is guaranteed with finite Koopman representations. We additionally address the practicalities associated with the data-driven implementation of the proposed approach, and demonstrate the proposed method on several numerical examples, including a robotic manipulator.