# Machine learning-based input-augmented Koopman modeling and predictive control of nonlinear processes

arXiv: https://arxiv.org/abs/2408.02315 · HTML: https://mlsanity.com/paper/2408.02315/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2024.

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

- [MAKO: Meta-Adaptive Koopman Operators for Learning-based Model Predictive Control of Parametrically Uncertain Nonlinear Systems](https://mlsanity.com/paper/2510.09042/) (2025)
- [Deep Neural Koopman Operator-based Economic Model Predictive Control of Shipboard Carbon Capture System](https://mlsanity.com/paper/2504.06818/) (2025)

## Abstract (arXiv)

Koopman-based modeling and model predictive control have been a promising alternative for optimal control of nonlinear processes. Good Koopman modeling performance significantly depends on an appropriate nonlinear mapping from the original state-space to a lifted state space. In this work, we propose an input-augmented Koopman modeling and model predictive control approach. Both the states and the known inputs are lifted using two deep neural networks (DNNs), and a Koopman model with nonlinearity in inputs is trained within the higher-dimensional state-space. A Koopman-based model predictive control problem is formulated. To bypass non-convex optimization induced by the nonlinearity in the Koopman model, we further present an iterative implementation algorithm, which approximates the optimal control input via solving a convex optimization problem iteratively. The proposed method is applied to a chemical process and a biological water treatment process via simulations. The efficacy and advantages of the proposed modeling and control approach are demonstrated.