# Leveraging Reinforcement Learning and Koopman Theory for Enhanced Model Predictive Control Performance

arXiv: https://arxiv.org/abs/2505.08122 · HTML: https://mlsanity.com/paper/2505.08122/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for autonomous driving and traffic, one of 15 directions in Deep reinforcement learning methods.
- Builds on 16 of its 35 references that are in the map.
- First posted on arXiv 12 May 2025.

## Placed in

- Deep reinforcement learning methods / [RL for autonomous driving and traffic](https://mlsanity.com/deeprl/rl-for-autonomous-driving-and-traffic/)

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Addressing Function Approximation Error in Actor-Critic Methods](https://mlsanity.com/paper/1802.09477/) (2018)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Implementation Matters in Deep Policy Gradients: A Case Study on PPO and TRPO](https://mlsanity.com/paper/2005.12729/) (2020)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Differentiating Through a Cone Program](https://mlsanity.com/paper/1904.09043/) (2019)
- [Data-driven Economic NMPC using Reinforcement Learning](https://mlsanity.com/paper/1904.04152/) (2019)
- [Generalizing Koopman Theory to allow for inputs and control](https://mlsanity.com/paper/1602.07647/) (2016)
- [Data-driven End-to-end Learning of Pole Placement Control for Nonlinear Dynamics via Koopman Invariant Subspaces](https://mlsanity.com/paper/2208.08883/) (2022)

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

- [Trustworthy and Explainable Deep Reinforcement Learning for Safe and Energy-Efficient Process Control: A Use Case in Industrial Compressed Air Systems](https://mlsanity.com/paper/2512.18317/) (2025)

## Abstract (arXiv)

This study presents an innovative approach to Model Predictive Control (MPC) by leveraging the powerful combination of Koopman theory and Deep Reinforcement Learning (DRL). By transforming nonlinear dynamical systems into a higher-dimensional linear regime, the Koopman operator facilitates the linear treatment of nonlinear behaviors, paving the way for more efficient control strategies. Our methodology harnesses the predictive prowess of Koopman-based models alongside the optimization capabilities of DRL, particularly using the Proximal Policy Optimization (PPO) algorithm, to enhance the controller's performance. The resulting end-to-end learning framework refines the predictive control policies to cater to specific operational tasks, optimizing both performance and economic efficiency. We validate our approach through rigorous NMPC and eNMPC case studies, demonstrating that the Koopman-RL controller outperforms traditional controllers by achieving higher stability, superior constraint satisfaction, and significant cost savings. The findings indicate that our model can be a robust tool for complex control tasks, offering valuable insights into future applications of RL in MPC.