Deep-Learning-Based Identification of LPV Models for Nonlinear Systems

TL;DR

This paper introduces a deep learning method for jointly estimating scheduling maps and LPV models of nonlinear systems from data, improving usability and providing theoretical guarantees.

Contribution

It presents a novel deep learning approach for simultaneous estimation of scheduling maps and LPV models with consistency guarantees.

Findings

Demonstrates effectiveness on a realistic identification problem.

Provides theoretical consistency guarantees.

Improves the usability of LPV modeling for nonlinear systems.

Abstract

The Linear Parameter-Varying (LPV) framework provides a modeling and control design toolchain to address nonlinear (NL) system behavior via linear surrogate models. Despite major research effort on LPV data-driven modeling, a key shortcoming of the current identification theory is that often the scheduling variable is assumed to be a given measured signal in the data set. In case of identifying an LPV model of a NL system, the selection of the scheduling map, which describes the relation to the measurable scheduling signal, is put on the users' shoulder, with only limited supporting tools available. This choice however greatly affects the usability and complexity of the resulting LPV model. This paper presents a deep-learning-based approach to provide joint estimation of a scheduling map and an LPV state-space model of a NL system from input-output data, and has consistency guarantees under general innovation-type noise conditions. Its efficiency is demonstrated on a realistic identification problem.