# Deep Koopman Economic Model Predictive Control of a Pasteurisation Unit

arXiv: https://arxiv.org/abs/2511.04437 · HTML: https://mlsanity.com/paper/2511.04437/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 6 Nov 2025.

## Builds on (most cited first, 10 of 10)

- [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)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Optimal construction of Koopman eigenfunctions for prediction and control](https://mlsanity.com/paper/1810.08733/) (2018)
- [Deep Learning of Koopman Representation for Control](https://mlsanity.com/paper/2010.07546/) (2020)
- [Deep Koopman Operator with Control for Nonlinear Systems](https://mlsanity.com/paper/2202.08004/) (2022)
- [End-to-End Reinforcement Learning of Koopman Models for Economic Nonlinear Model Predictive Control](https://mlsanity.com/paper/2308.01674/) (2023)
- [Koopman-based Differentiable Predictive Control for the Dynamics-Aware Economic Dispatch Problem](https://mlsanity.com/paper/2203.08984/) (2022)
- [Efficient Economic Model Predictive Control of Water Treatment Process with Learning-based Koopman Operator](https://mlsanity.com/paper/2405.12478/) (2024)

## Abstract (arXiv)

This paper presents a deep Koopman-based Economic Model Predictive Control (EMPC) for efficient operation of a laboratory-scale pasteurization unit (PU). The method uses Koopman operator theory to transform the complex, nonlinear system dynamics into a linear representation, enabling the application of convex optimization while representing the complex PU accurately. The deep Koopman model utilizes neural networks to learn the linear dynamics from experimental data, achieving a 45% improvement in open-loop prediction accuracy over conventional N4SID subspace identification. Both analyzed models were employed in the EMPC formulation that includes interpretable economic costs, such as energy consumption, material losses due to inadequate pasteurization, and actuator wear. The feasibility of EMPC is ensured using slack variables. The deep Koopman EMPC and N4SID EMPC are numerically validated on a nonlinear model of multivariable PU under external disturbance. The disturbances include feed pump fail-to-close scenario and the introduction of a cold batch to be pastuerized. These results demonstrate that the deep Koopmand EMPC achieves a 32% reduction in total economic cost compared to the N4SID baseline. This improvement is mainly due to the reductions in material losses and energy consumption. Furthermore, the steady-state operation via Koopman-based EMPC requires 10.2% less electrical energy. The results highlight the practical advantages of integrating deep Koopman representations with economic optimization to achieve resource-efficient control of thermal-intensive plants.