# Learning Neural Feedback Linearization for Data-driven Systems via Augmented Lagrangian

arXiv: https://arxiv.org/abs/2609.25163 · HTML: https://mlsanity.com/paper/2609.25163/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 37 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [Feedback Linearization based on Gaussian Processes with event-triggered Online Learning](https://mlsanity.com/paper/1911.06565/) (2019)
- [Willems' Fundamental Lemma for State-space Systems and its Extension to Multiple Datasets](https://mlsanity.com/paper/2002.01023/) (2020)
- [Data-based Control of Feedback Linearizable Systems](https://mlsanity.com/paper/2204.01148/) (2022)
- [Data-Driven Feedback Linearization using the Koopman Generator](https://mlsanity.com/paper/2210.05046/) (2022)
- [Data-driven Stabilization of SISO Feedback Linearizable Systems](https://mlsanity.com/paper/2003.14240/) (2020)
- [Controller Synthesis from Noisy-Input Noisy-Output Data](https://mlsanity.com/paper/2402.02588/) (2024)
- [A Taxonomy of Numerical Differentiation Methods](https://mlsanity.com/paper/2512.09090/) (2025)
- [Data-driven system analysis of nonlinear systems using polynomial approximation](https://mlsanity.com/paper/2108.11298/) (2021)
- [Feedback linearization through the lens of data](https://mlsanity.com/paper/2308.11229/) (2023)
- [Identification For Control Based on Neural Networks: Approximately Linearizable Models](https://mlsanity.com/paper/2409.15858/) (2024)
- [Data driven feedback linearization of nonlinear control systems via Lie derivatives and stacked regression approach](https://mlsanity.com/paper/2508.13241/) (2025)

## Abstract (arXiv)

The paper proposes a novel data-driven framework for designing and training a feedback linearizing controller by explicitly incorporating relative degree based conditions into the learning process. This enables the conventional feedback controller components to be replaced by neural Lie derivatives, thereby facilitating a fully data-driven feedback linearization framework. Furthermore, practical closed-loop stability is established by deriving sufficient conditions under which bounded identification errors lead to bounded tracking errors. The derived theoretical results are validated through their application to an armature controlled DC motor.