# Efficient Economic Model Predictive Control of Water Treatment Process with Learning-based Koopman Operator

arXiv: https://arxiv.org/abs/2405.12478 · HTML: https://mlsanity.com/paper/2405.12478/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2024.

## Built on by (most cited first, 2 of 2)

- [Deep Neural Koopman Operator-based Economic Model Predictive Control of Shipboard Carbon Capture System](https://mlsanity.com/paper/2504.06818/) (2025)
- [Deep Koopman Economic Model Predictive Control of a Pasteurisation Unit](https://mlsanity.com/paper/2511.04437/) (2025)

## Abstract (arXiv)

Used water treatment plays a pivotal role in advancing environmental sustainability. Economic model predictive control holds the promise of enhancing the overall operational performance of the water treatment facilities. In this study, we propose a data-driven economic predictive control approach within the Koopman modeling framework. First, we propose a deep learning-enabled input-output Koopman modeling approach, which predicts the overall economic operational cost of the wastewater treatment process based on input data and available output measurements that are directly linked to the operational costs. Subsequently, by leveraging this learned input-output Koopman model, a convex economic predictive control scheme is developed. The resulting predictive control problem can be efficiently solved by leveraging quadratic programming solvers, and complex non-convex optimization problems are bypassed. The proposed method is applied to a benchmark wastewater treatment process. The proposed method significantly improves the overall economic operational performance of the water treatment process. Additionally, the computational efficiency of the proposed method is significantly enhanced as compared to benchmark control solutions.