Efficient Learning of Affine and Rational Dependency LPV Models With Linear Fractional Representation

TL;DR

This paper introduces a novel LPV modeling approach with rational scheduling dependency using Linear Fractional Representation, enabling efficient modeling of complex nonlinear systems from input-output data.

Contribution

It proposes a direct parameterization for rational LPV-LFR models and a joint-estimation method, improving modeling efficiency over affine models.

Findings

Accurate modeling demonstrated on two simulation examples.

Fewer scheduling variables needed compared to affine models.

Abstract

Identifying control-friendly models of nonlinear systems remains one of the major challenges at the intersection of system identification and control. The Linear Parameter-Varying (LPV) framework offers a promising solution, but existing identification methods often rely on model structures with affine scheduling dependency. Instead, this work proposes the use of LPV models with Linear Fractional Representation (LFR) admitting a rational scheduling-dependency, capable of modelling complex nonlinear systems with fewer scheduling variables compared to affine models. This work introduces a direct parameterization to ensure well-posedness of rational LPV-LFR models, which by joint-estimation of an LPV plant and scheduling map, using only input-output data, is capable of modelling complex nonlinear systems. Accuracy of the proposed approach is shown on two simulation examples.