# Robust data-driven control for nonlinear systems using the Koopman operator

arXiv: https://arxiv.org/abs/2304.03519 · HTML: https://mlsanity.com/paper/2304.03519/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2023.

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

- [Nonparametric Control Koopman Operators](https://mlsanity.com/paper/2405.07312/) (2024)
- [SafEDMD: A Koopman-based data-driven controller design framework for nonlinear dynamical systems](https://mlsanity.com/paper/2402.03145/) (2024)
- [Data-Driven Stochastic Optimal Control in Reproducing Kernel Hilbert Spaces](https://mlsanity.com/paper/2407.16407/) (2024)
- [Uncertainty Modelling and Robust Observer Synthesis using the Koopman Operator](https://mlsanity.com/paper/2410.01057/) (2024)
- [Input-Side Variance Suppression under Non-Normal Transient Amplification in Continuous-Control Reinforcement Learning](https://mlsanity.com/paper/2604.17744/) (2026)
- [KOALA: Koopman Operator Learning for WiFi-Based Anticipatory Hum](https://mlsanity.com/paper/2608.15815/) (2026)

## Abstract (arXiv)

Data-driven analysis and control of dynamical systems have gained a lot of interest in recent years. While the class of linear systems is well studied, theoretical results for nonlinear systems are still rare. In this paper, we present a data-driven controller design method for discrete-time control-affine nonlinear systems. Our approach relies on the Koopman operator, which is a linear but infinite-dimensional operator lifting the nonlinear system to a higher-dimensional space. Particularly, we derive a linear fractional representation of a lifted bilinear system representation based on measured data. Further, we restrict the lifting to finite dimensions, but account for the truncation error using a finite-gain argument. We derive a linear matrix inequality based design procedure to guarantee robust local stability for the resulting bilinear system for all error terms satisfying the finite-gain bound and, thus, also for the underlying nonlinear system. Finally, we apply the developed design method to the nonlinear Van der Pol oscillator.