Linear Parameter-Varying Embedding of Nonlinear Models with Reduced Conservativeness

TL;DR

This paper presents a systematic method to embed nonlinear systems into LPV models with reduced conservativeness by combining polynomial approximation, residual analysis, and PCA for scheduling parameter selection.

Contribution

The paper introduces a novel LPV embedding approach that jointly optimizes model accuracy and complexity, reducing conservativeness compared to existing methods.

Findings

Effective LPV embedding of nonlinear systems demonstrated on robotic manipulator

Reduced conservativeness compared to previous LPV modeling approaches

Method shows promising results in balancing model accuracy and complexity

Abstract

In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are approximated using multivariate polynomial regression. Taking into account the residuals of the approximation as the potential scheduling parameters, a principle component analysis (PCA) is conducted to introduce a limited set of auxiliary scheduling parameters in coping with the trade-o? between model accuracy and complexity. In this way, LPV embedding of the nonlinear systems and scheduling variable selection are jointly performed such that a good trade-o? between complexity and conservativeness can be found. The developed LPV model depends polynomially on some of the state variables and affinely on the introduced auxiliary scheduling variables, which all together comprise the overall scheduling vector. The methodology is applied to a two-degree of freedom (2-DOf) robotic manipulator in addition to an academic example to reveal the effectiveness of the proposed method and to show the merits of the presented approach compared with some available results in the literature.