Koopman operator theory provides a linear model of a dynamical system in the infinite dimensional space. In this post, I have summarized some basics of the Koopman operator and its extention to control systems.

By finding the Koopman operator of a dynamical (control) system, we can leverage existing and well-studied theory in linear systems to approach any nonlinear systems. Koopman operator theory also provides a data-driven control method.

More details can be found in Koopman operator slides.

Fig. 1: Outline of Koopman operator theory slides.