From Nonlinear Identification to Linear Parameter Varying Models: Benchmark Examples

TL;DR

This paper introduces a systematic data-driven method to identify LPV models from nonlinear systems using fractional representations, simplifying scheduling variable selection and improving robustness against measurement noise.

Contribution

It presents a novel LPV embedding approach from nonlinear fractional models, enabling easier scheduling variable selection and noise-robust estimation.

Findings

Successful application on benchmark examples

Improved scheduling variable identification

Robustness to measurement noise

Abstract

Linear parameter-varying (LPV) models form a powerful model class to analyze and control a (nonlinear) system of interest. Identifying a LPV model of a nonlinear system can be challenging due to the difficulty of selecting the scheduling variable(s) a priori, which is quite challenging in case a first principles based understanding of the system is unavailable. This paper presents a systematic LPV embedding approach starting from nonlinear fractional representation models. A nonlinear system is identified first using a nonlinear block-oriented linear fractional representation (LFR) model. This nonlinear LFR model class is embedded into the LPV model class by factorization of the static nonlinear block present in the model. As a result of the factorization a LPV-LFR or a LPV state-space model with an affine dependency results. This approach facilitates the selection of the scheduling variable from a data-driven perspective. Furthermore the estimation is not affected by measurement noise on the scheduling variables, which is often left untreated by LPV model identification methods. The proposed approach is illustrated on two well-established nonlinear modeling benchmark examples.