# Model-Based Control Using Koopman Operators

arXiv: https://arxiv.org/abs/1709.01568 · HTML: https://mlsanity.com/paper/1709.01568/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Sep 2017.

## Built on by (most cited first, 14 of 14)

- [Task-Oriented Koopman-Based Control with Contrastive Encoder](https://mlsanity.com/paper/2309.16077/) (2023)
- [Vision-based system identification and 3D keypoint discovery using dynamics constraints](https://mlsanity.com/paper/2109.05928/) (2021)
- [System Norm Regularization Methods for Koopman Operator Approximation](https://mlsanity.com/paper/2110.09658/) (2021)
- [Linear quadratic control of nonlinear systems with Koopman operator learning and the Nystr"om method](https://mlsanity.com/paper/2403.02811/) (2024)
- [Discriminant Dynamic Mode Decomposition for Labeled Spatio-Temporal Data Collections](https://mlsanity.com/paper/2102.09973/) (2021)
- [Physics-Informed Kernel Embeddings: Integrating Prior System Knowledge with Data-Driven Control](https://mlsanity.com/paper/2301.03565/) (2023)
- [Closed-Loop Koopman Operator Approximation](https://mlsanity.com/paper/2303.15318/) (2023)
- [Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator](https://mlsanity.com/paper/2410.01057/) (2024)
- [KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning](https://mlsanity.com/paper/2509.09074/) (2025)
- [Learn Proportional Derivative Controllable Latent Space from Pixels](https://mlsanity.com/paper/2110.08239/) (2021)
- [Koopman pose predictions for temporally consistent human walking estimations](https://mlsanity.com/paper/2205.02737/) (2022)
- [Physical Backdoor Trigger Activation of Autonomous Vehicle using Reachability Analysis](https://mlsanity.com/paper/2303.13992/) (2023)
- [Analysis of Truncated Singular Value Decomposition for Koopman Operator-Based Lane Change Model](https://mlsanity.com/paper/2409.18586/) (2024)
- [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 explores the application of Koopman operator theory to the control of robotic systems. The operator is introduced as a method to generate data-driven models that have utility for model-based control methods. We then motivate the use of the Koopman operator towards augmenting model-based control. Specifically, we illustrate how the operator can be used to obtain a linearizable data-driven model for an unknown dynamical process that is useful for model-based control synthesis. Simulated results show that with increasing complexity in the choice of the basis functions, a closed-loop controller is able to invert and stabilize a cart- and VTOL-pendulum systems. Furthermore, the specification of the basis function are shown to be of importance when generating a Koopman operator for specific robotic systems. Experimental results with the Sphero SPRK robot explore the utility of the Koopman operator in a reduced state representation setting where increased complexity in the basis function improve open- and closed-loop controller performance in various terrains, including sand.