  We use Koopman theory for data-driven model reduction of nonlinear dynamical
systems with controls. We propose generic model structures combining
delay-coordinate encoding of measurements and full-state decoding to integrate
reduced Koopman modeling and state estimation. We present a deep-learning
approach to train the proposed models. A case study demonstrates that our
approach provides accurate control models and enables real-time capable
nonlinear model predictive control of a high-purity cryogenic distillation
column.
