  The Koopman operator serves as the theoretical backbone for machine learning
of dynamical control systems, where the operator is heuristically approximated
by extended dynamic mode decomposition (EDMD). In this paper, we propose
Stability- and certificate-oriented EDMD (SafEDMD): a novel EDMD-based learning
architecture which comes along with rigorous certificates, resulting in a
reliable surrogate model generated in a data-driven fashion. To ensure the
trustworthiness of SafEDMD, we derive proportional error bounds, which vanish
at the origin and are tailored to control tasks, leading to certified
controller design based on semi-definite programming. We illustrate the
developed method by means of several benchmark examples and highlight the
advantages over state-of-the-art methods.
