# Model Predictive Control of a Vehicle using Koopman Operator

arXiv: https://arxiv.org/abs/2103.04978 · HTML: https://mlsanity.com/paper/2103.04978/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2021.

## Built on by (most cited first, 6 of 6)

- [End-to-End Reinforcement Learning of Koopman Models for Economic Nonlinear Model Predictive Control](https://mlsanity.com/paper/2308.01674/) (2023)
- [Towards Data-driven LQR with Koopmanizing Flows](https://mlsanity.com/paper/2201.11640/) (2022)
- [Data-Driven Encoding: A New Numerical Method for Computation of the Koopman Operator](https://mlsanity.com/paper/2301.06542/) (2023)
- [Deep Bilinear Koopman Model for Real-Time Vehicle Control in Frenet Frame](https://mlsanity.com/paper/2507.12578/) (2025)
- [To Learn or Not to Learn: A Litmus Test for Using Reinforcement Learning in Control](https://mlsanity.com/paper/2604.11463/) (2026)
- [MetaKoopman: Bayesian Meta-Learning of Koopman Operators for Modeling Structured Dynamics under Distribution Shifts](https://mlsanity.com/paper/2607.26345/) (2026)

## Abstract (arXiv)

This paper continues in the work from arXiv:1903.06103 [math.OC] where a nonlinear vehicle model was approximated in a purely data-driven manner by a linear predictor of higher order, namely the Koopman operator. The vehicle system typically features a lot of nonlinearities such as rigid-body dynamics, coordinate system transformations and most importantly the tire. These nonlinearities are approximated in a predefined subset of the state-space by the linear Koopman operator and used for a linear Model Predictive Control (MPC) design in the high-dimension state space where the nonlinear system dynamics evolve linearly. The result is a nonlinear MPC designed by linear methodologies. It is demonstrated that the Koopman-based controller is able to recover from a very unusual state of the vehicle where all the aforementioned nonlinearities are dominant. The controller is compared with a controller based on a classic local linearization and shortcomings of this approach are discussed.