# Deep Neural Koopman Operator-based Economic Model Predictive Control of Shipboard Carbon Capture System

arXiv: https://arxiv.org/abs/2504.06818 · HTML: https://mlsanity.com/paper/2504.06818/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 77 references that are in the map.
- First posted on arXiv 9 Apr 2025.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Learning to Adapt in Dynamic, Real-World Environments Through Meta-Reinforcement Learning](https://mlsanity.com/paper/1803.11347/) (2018)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Learning Deep Neural Network Representations for Koopman Operators of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1708.06850/) (2017)
- [Generalizing Koopman Theory to allow for inputs and control](https://mlsanity.com/paper/1602.07647/) (2016)
- [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)
- [Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control](https://mlsanity.com/paper/1911.08751/) (2019)
- [Robust Tube-based Model Predictive Control with Koopman Operators--Extended Version](https://mlsanity.com/paper/2108.13011/) (2021)
- [End-to-End Reinforcement Learning of Koopman Models for Economic Nonlinear Model Predictive Control](https://mlsanity.com/paper/2308.01674/) (2023)
- [Constraint-Tightening and Stability in Stochastic Model Predictive Control](https://mlsanity.com/paper/1511.03488/) (2015)
- [On the Optimality and Convergence Properties of the Iterative Learning Model Predictive Controller](https://mlsanity.com/paper/2010.15153/) (2020)
- [Modeling and Control of Diesel Engine Emissions using Multi-layer Neural Networks and Economic Model Predictive Control](https://mlsanity.com/paper/2311.03552/) (2023)
- [Reduced-order Koopman modeling and predictive control of nonlinear processes](https://mlsanity.com/paper/2404.00553/) (2024)
- [Incorporating ESO into Deep Koopman Operator Modelling for Control of Autonomous Vehicles](https://mlsanity.com/paper/2405.10157/) (2024)
- [Efficient Economic Model Predictive Control of Water Treatment Process with Learning-based Koopman Operator](https://mlsanity.com/paper/2405.12478/) (2024)
- [Machine learning-based input-augmented Koopman modeling and predictive control of nonlinear processes](https://mlsanity.com/paper/2408.02315/) (2024)
- [Robust Economic Model Predictive Control without Terminal Conditions](https://mlsanity.com/paper/1911.12235/) (2019)
- [Deep Koopman Operator-Informed Safety Command Governor for Autonomous Vehicles](https://mlsanity.com/paper/2405.10145/) (2024)
- [Machine learning-based hybrid dynamic modeling and economic predictive control of carbon capture process for ship decarbonization](https://mlsanity.com/paper/2502.05833/) (2025)

## Abstract (arXiv)

Shipboard carbon capture is a promising solution to help reduce carbon emissions in international shipping. In this work, we propose a data-driven dynamic modeling and economic predictive control approach within the Koopman framework. This integrated modeling and control approach is used to achieve safe and energy-efficient process operation of shipboard post-combustion carbon capture plants. Specifically, we propose a deep neural Koopman operator modeling approach, based on which a Koopman model with time-varying model parameters is established. This Koopman model predicts the overall economic operational cost and key system outputs, based on accessible partial state measurements. By leveraging this learned model, a constrained economic predictive control scheme is developed. Despite time-varying parameters involved in the formulated model, the formulated optimization problem associated with the economic predictive control design is convex, and it can be solved efficiently during online control implementations. Extensive tests are conducted on a high-fidelity simulation environment for shipboard post-combustion carbon capture processes. Four ship operational conditions are taken into account. The results show that the proposed method significantly improves the overall economic operational performance and carbon capture rate. Additionally, the proposed method guarantees safe operation by ensuring that hard constraints on the system outputs are satisfied.