# Data-driven Nonlinear Model Reduction using Koopman Theory: Integrated Control Form and NMPC Case Study

arXiv: https://arxiv.org/abs/2401.04508 · HTML: https://mlsanity.com/paper/2401.04508/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 9 Jan 2024.

## Builds on (most cited first, 5 of 5)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Linear identification of nonlinear systems: A lifting technique based on the Koopman operator](https://mlsanity.com/paper/1605.04457/) (2016)
- [Willems' fundamental lemma for linear descriptor systems and its use for data-driven output-feedback MPC](https://mlsanity.com/paper/2202.07930/) (2022)

## Built on by (most cited first, 1 of 1)

- [Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison](https://mlsanity.com/paper/2506.12819/) (2025)

## Abstract (arXiv)

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.