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

2025-02-04

AI Summary

Identifying large-scale linear parameter-varying (LPV) systems is challenging due to high computational cost and the need for intrusive system access or full-order models. Method: This paper proposes DMD-LPV, a non-intrusive model order reduction (MOR) method for LPV systems based on dynamic mode decomposition (DMD). It is the first approach to extend DMD to the LPV identification framework, enabling data-driven construction of both local and global LPV models under known structural assumptions—without requiring full-order simulations or system modifications. Parameter dependence is modeled via polynomials, and the method is validated on a discretized linear diffusion equation. Results: Experiments demonstrate that DMD-LPV efficiently generates high-fidelity reduced-order LPV models for large-scale diffusion systems. Identification avoids full-order computations entirely, and model accuracy degradation is negligible. The method significantly enhances the feasibility and computational efficiency of LPV modeling for large-scale systems.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: (Large) Language Models

Application Category

• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

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.

Problem

• Identify large-scale LPV systems
• Use Dynamic Mode Decomposition
• Develop reduced-order modeling method

Innovation

• DMD-LPV for large-scale systems
• Nonintrusive reduced-order modeling
• Efficient LPV model identification