# On the Initialization of Nonlinear LFR Model Identification with the Best Linear Approximation

arXiv: https://arxiv.org/abs/2004.05040 · HTML: https://mlsanity.com/paper/2004.05040/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Apr 2020.

## Built on by (most cited first, 9 of 9)

- [Deep Subspace Encoders for Nonlinear System Identification](https://mlsanity.com/paper/2210.14816/) (2022)
- [Improved Initialization of State-Space Artificial Neural Networks](https://mlsanity.com/paper/2103.14516/) (2021)
- [Meta-Learning for Physically-Constrained Neural System Identification](https://mlsanity.com/paper/2501.06167/) (2025)
- [On feedforward control using physics-guided neural networks: Training cost regularization and optimized initialization](https://mlsanity.com/paper/2201.12088/) (2022)
- [Initialization Approach for Nonlinear State-Space Identification via the Subspace Encoder Approach](https://mlsanity.com/paper/2304.02119/) (2023)
- [Orthogonal projection-based regularization for efficient model augmentation](https://mlsanity.com/paper/2501.05842/) (2025)
- [Identification of the nonlinear steering dynamics of an autonomous vehicle](https://mlsanity.com/paper/2105.04529/) (2021)
- [State Derivative Normalization for Continuous-Time Deep Neural Networks](https://mlsanity.com/paper/2401.02902/) (2024)
- [Learning Surrogate LPV State-Space Models with Uncertainty Quantification](https://mlsanity.com/paper/2603.29532/) (2026)

## Abstract (arXiv)

Balancing the model complexity and the representation capability towards the process to be captured remains one of the main challenges in nonlinear system identification. One possibility to reduce model complexity is to impose structure on the model representation. To this end, this work considers the linear fractional representation framework. In a linear fractional representation the linear dynamics and the system nonlinearities are modeled by two separate blocks that are interconnected with one another. This results in a structured, yet flexible model structure. Estimating such a model directly from input-output data is not a trivial task as the involved optimization is nonlinear in nature. This paper proposes an initialization scheme for the model parameters based on the best linear approximation of the system and shows that this approach results in high quality models on a set of benchmark data sets.