A behavioral approach for LPV data-driven representations

TL;DR

This paper introduces a novel data-driven representation for LPV systems using the behavioral approach, enabling direct analysis and control based solely on data, with a rank-based test for data completeness.

Contribution

It develops a behavioral data-driven representation for LPV systems with a kernel structure and provides a rank test to verify data sufficiency for finite-horizon behavior.

Findings

Provides a necessary and sufficient rank-based test for data completeness.

Enables direct data-driven simulation of LPV systems.

Demonstrates applicability to LPV embeddings of nonlinear systems.

Abstract

In this paper, we present a data-driven representation for linear parameter-varying (LPV) systems, which can be used for direct data-driven analysis and control of such systems. Specifically, we use the behavioral approach to develop a data-driven representation of the finite-horizon behavior of LPV systems for which there exists a kernel representation with shifted-affine scheduling dependence. Moreover, we provide a necessary and sufficient rank-based test on the available data that concludes whether the data fully represents the finite-horizon LPV behavior. Using the proposed data-driven representation, we also solve the data-driven simulation problem for LPV systems. Through multiple examples, we demonstrate that the results in this paper allow us to formulate a novel set of direct data-driven analysis and control methods for LPV systems, which are also applicable for LPV embeddings of nonlinear systems.