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

TL;DR

This paper introduces DMD-LPV, a novel data-driven method inspired by Dynamic Mode Decomposition, for efficiently identifying large-scale Linear Parameter Varying systems through reduced-order modeling, with validated results on a diffusion equation example.

Contribution

The paper develops a new methodology for large-scale LPV system identification using nonintrusive reduced-order modeling based on DMD, addressing a gap in existing literature.

Findings

Successfully identified reduced-order LPV models of large-scale systems.

Method performs well with minimal performance loss during reduction.

Validated on a discretized diffusion equation example.

Abstract

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.