# Discrete-Time Nonlinear Feedback Linearization via Physics-Informed Machine Learning

arXiv: https://arxiv.org/abs/2303.08884 · HTML: https://mlsanity.com/paper/2303.08884/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 59 references that are in the map.
- First posted on arXiv 15 Mar 2023.

## Builds on (most cited first, 5 of 5)

- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons](https://mlsanity.com/paper/2201.07766/) (2022)
- [Parsimonious Physics-Informed Random Projection Neural Networks for Initial-Value Problems of ODEs and index-1 DAEs](https://mlsanity.com/paper/2203.05337/) (2022)
- [Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach](https://mlsanity.com/paper/2207.05779/) (2022)
- [Neural network architectures using min-plus algebra for solving certain high dimensional optimal control problems and Hamilton-Jacobi PDEs](https://mlsanity.com/paper/2105.03336/) (2021)

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

- [RandONet: Shallow-Networks with Random Projections for learning linear and nonlinear operators](https://mlsanity.com/paper/2406.05470/) (2024)
- [Nonlinear Discrete-Time Observers with Physics-Informed Neural Networks](https://mlsanity.com/paper/2402.12360/) (2024)
- [Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators](https://mlsanity.com/paper/2509.23975/) (2025)
- [Stability and Bifurcation Analysis of Nonlinear PDEs via Random Projection-based PINNs: A Krylov-Arnoldi Approach](https://mlsanity.com/paper/2603.21568/) (2026)

## Abstract (arXiv)

We present a physics-informed machine learning (PIML) scheme for the feedback linearization of nonlinear discrete-time dynamical systems. The PIML finds the nonlinear transformation law, thus ensuring stability via pole placement, in one step. In order to facilitate convergence in the presence of steep gradients in the nonlinear transformation law, we address a greedy-wise training procedure. We assess the performance of the proposed PIML approach via a benchmark nonlinear discrete map for which the feedback linearization transformation law can be derived analytically; the example is characterized by steep gradients, due to the presence of singularities, in the domain of interest. We show that the proposed PIML outperforms, in terms of numerical approximation accuracy, the traditional numerical implementation, which involves the construction--and the solution in terms of the coefficients of a power-series expansion--of a system of homological equations as well as the implementation of the PIML in the entire domain, thus highlighting the importance of continuation techniques in the training procedure of PIML.