# Identifying Large-Scale Linear Parameter Varying Systems with Dynamic Mode Decomposition Methods

arXiv: https://arxiv.org/abs/2502.02336 · HTML: https://mlsanity.com/paper/2502.02336/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 28 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 4 of 4)

- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Kernel Learning for Robust Dynamic Mode Decomposition: Linear and Nonlinear Disambiguation Optimization (LANDO)](https://mlsanity.com/paper/2106.01510/) (2021)
- [Investigation of Proper Orthogonal Decomposition for Echo State Networks](https://mlsanity.com/paper/2211.17179/) (2022)
- [Linear Parameter-Varying Control of Nonlinear Systems based on Incremental Stability](https://mlsanity.com/paper/1909.07154/) (2019)

## Abstract (arXiv)

Linear Parameter Varying (LPV) Systems are a well-established class of nonlinear systems with a rich theory for stability analysis, control, and analytical response finding, among other aspects. Although there are works on data-driven identification of such systems, the literature is quite scarce in terms of works that tackle the identification of LPV models for large-scale systems. Since large-scale systems are ubiquitous in practice, this work develops a methodology for the local and global identification of large-scale LPV systems based on nonintrusive reduced-order modeling. The developed method is coined as DMD-LPV for being inspired in the Dynamic Mode Decomposition (DMD). To validate the proposed identification method, we identify a system described by a discretized linear diffusion equation, with the diffusion gain defined by a polynomial over a parameter. The experiments show that the proposed method can easily identify a reduced-order LPV model of a given large-scale system without the need to perform identification in the full-order dimension, and with almost no performance decay over performing a reduction, given that the model structure is well-established.