# Data-based Control of Feedback Linearizable Systems

arXiv: https://arxiv.org/abs/2204.01148 · HTML: https://mlsanity.com/paper/2204.01148/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Apr 2022.

## Built on by (most cited first, 4 of 4)

- [Exploring the Links between the Fundamental Lemma and Kernel Regression](https://mlsanity.com/paper/2403.05368/) (2024)
- [From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma](https://mlsanity.com/paper/2508.07494/) (2025)
- [Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes](https://mlsanity.com/paper/2501.15849/) (2025)
- [Learning Neural Feedback Linearization for Data-driven Systems via Augmented Lagrangian](https://mlsanity.com/paper/2609.25163/) (2026)

## Abstract (arXiv)

We present an extension of Willems' Fundamental Lemma to the class of multi-input multi-output discrete-time feedback linearizable nonlinear systems, thus providing a data-based representation of their input-output trajectories. Two sources of uncertainty are considered. First, the unknown linearizing input is inexactly approximated by a set of basis functions. Second, the measured output data is contaminated by additive noise. Further, we propose an approach to approximate the solution of the data-based simulation and output matching problems, and show that the difference from the true solution is bounded. Finally, the results are illustrated on an example of a fully-actuated double inverted pendulum.