# Data driven feedback linearization of nonlinear control systems via Lie derivatives and stacked regression approach

arXiv: https://arxiv.org/abs/2508.13241 · HTML: https://mlsanity.com/paper/2508.13241/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 18 Aug 2025.

## Builds on (most cited first, 9 of 9)

- [Sparse identification of nonlinear dynamics for model predictive control in the low-data limit](https://mlsanity.com/paper/1711.05501/) (2017)
- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach](https://mlsanity.com/paper/2105.04869/) (2021)
- [Feedback Linearization based on Gaussian Processes with event-triggered Online Learning](https://mlsanity.com/paper/1911.06565/) (2019)
- [From noisy data to feedback controllers: non-conservative design via a matrix S-lemma](https://mlsanity.com/paper/2006.00870/) (2020)
- [Willems' Fundamental Lemma for State-space Systems and its Extension to Multiple Datasets](https://mlsanity.com/paper/2002.01023/) (2020)
- [Robust data-driven state-feedback design](https://mlsanity.com/paper/1909.04314/) (2019)
- [Learning Controllers from Data via Approximate Nonlinearity Cancellation](https://mlsanity.com/paper/2201.10232/) (2022)
- [Learning controllers from data via kernel-based interpolation](https://mlsanity.com/paper/2304.09577/) (2023)

## Built on by (most cited first, 1 of 1)

- [Learning Neural Feedback Linearization for Data-driven Systems via Augmented Lagrangian](https://mlsanity.com/paper/2609.25163/) (2026)

## Abstract (arXiv)

Discovering the governing equations of a physical system and designing an effective feedback controller remains one of the most challenging and intensive areas of ongoing research. This task demands a deep understanding of the system behavior, including the nonlinear factors that influence its dynamics. In this article, we propose a novel methodology for identifying a feedback linearized physical system based on known prior dynamic behavior. Initially, the system is identified using a sparse regression algorithm, subsequently a feedback controller is designed for the discovered system by applying Lie derivatives to the dictionary of output functions to derive an augmented constraint which guarantees that no internal dynamics are observed. Unlike the prior related works, the novel aspect of this article combines the approach of stacked regression algorithm and relative degree conditions to discover and feedback linearize the true governing equations of a physical model.