# Multi-Step Deep Koopman Network (MDK-Net) for Vehicle Control in Frenet Frame

arXiv: https://arxiv.org/abs/2503.03002 · HTML: https://mlsanity.com/paper/2503.03002/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Deep Koopman Operator with Control for Nonlinear Systems](https://mlsanity.com/paper/2202.08004/) (2022)
- [Deep Neural Networks with Koopman Operators for Modeling and Control of Autonomous Vehicles](https://mlsanity.com/paper/2007.02219/) (2020)
- [Vehicular Applications of Koopman Operator Theory -- A Survey](https://mlsanity.com/paper/2303.10471/) (2023)
- [DDK: A Deep Koopman Approach for Dynamics Modeling and Trajectory Tracking of Autonomous Vehicles](https://mlsanity.com/paper/2110.14700/) (2021)
- [An Automatic Tuning MPC with Application to Ecological Cruise Control](https://mlsanity.com/paper/2309.09358/) (2023)

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

- [Enhanced Vehicle Speed Detection Considering Lane Recognition Using Drone Videos in California](https://mlsanity.com/paper/2506.11239/) (2025)
- [Deep Bilinear Koopman Model for Real-Time Vehicle Control in Frenet Frame](https://mlsanity.com/paper/2507.12578/) (2025)

## Abstract (arXiv)

The highly nonlinear dynamics of vehicles present a major challenge for the practical implementation of optimal and Model Predictive Control (MPC) approaches in path planning and following. Koopman operator theory offers a global linear representation of nonlinear dynamical systems, making it a promising framework for optimization-based vehicle control. This paper introduces a novel deep learning-based Koopman modeling approach that employs deep neural networks to capture the full vehicle dynamics-from pedal and steering inputs to chassis states-within a curvilinear Frenet frame. The superior accuracy of the Koopman model compared to identified linear models is shown for a double lane change maneuver. Furthermore, it is shown that an MPC controller deploying the Koopman model provides significantly improved performance while maintaining computational efficiency comparable to a linear MPC.