Machine Learning Barycenter Approach to Identifying LPV State-Space Models

TL;DR

This paper introduces a novel LPV model identification method using LS-SVM with a parameterization that incorporates filter poles, improving performance over traditional LPV-ARX models, demonstrated through simulation.

Contribution

The paper presents a new LS-SVM-based identification approach for LPV state-space models with a filter design and data-driven tuning, enhancing model accuracy.

Findings

Nonlinear dependencies on scheduling signals are effectively learned.

Significant performance improvements over traditional LPV-ARX models.

The method successfully handles complex nonlinearities in simulated examples.

Abstract

In this paper an identification method for state-space LPV models is presented. The method is based on a particular parameterization that can be written in linear regression form and enables model estimation to be handled using Least-Squares Support Vector Machine (LS-SVM). The regression form has a set of design variables that act as filter poles to the underlying basis functions. In order to preserve the meaning of the Kernel functions (crucial in the LS-SVM context), these are filtered by a 2D-system with the predictor dynamics. A data-driven, direct optimization based approach for tuning this filter is proposed. The method is assessed using a simulated example and the results obtained are twofold. First, in spite of the difficult nonlinearities involved, the nonparametric algorithm was able to learn the underlying dependencies on the scheduling signal. Second, a significant improvement in the performance of the proposed method is registered, if compared with the one achieved by placing the predictor poles at the origin of the complex plane, which is equivalent to considering an estimator based on an LPV auto-regressive (LPV-ARX) structure.