Deep Learning-based Identification of Koopman Models with Inputs

In recent years, there has been a growing interest in the development of global linear embeddings of nonlinear dynamical systems. A possible solution is given by the Koopman framework. The main idea is to lift the nonlinear system to a possibly infinite dimensional, but linear, space where the dynamics are governed by a so-called Koopman operator. In practice, only a limited number of lifting functions
(called observables) can be used. However, as the choice is generally ad-hoc, there is no guarantee on the approximation capability. Furthermore, in its original formulation, the Koopman framework only addresses autonomous systems. In the present work, we aim to address these shortcomings.