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.

翻译：我们利用Koopman理论对带控制的非线性动力学系统进行数据驱动的模型降阶。通过结合测量值的延迟坐标编码与全状态解码，我们提出了通用的模型结构，将降阶Koopman建模与状态估计相集成。我们提出了一种基于深度学习的方法来训练所提出的模型。案例研究表明，该方法能够提供精确的控制模型，并实现高纯度低温精馏塔的实时非线性模型预测控制。