A behavioral approach for LPV data-driven representations

Chris Verhoek; Ivan Markovsky; Sofie Haesaert; Roland Tóth

doi:10.1109/TAC.2025.3613909

A behavioral approach for LPV data-driven representations

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2 Citations (SciVal)

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.

Original language	English
Article number	11177019
Journal	IEEE Transactions on Automatic Control
Volume	XX
DOIs	https://doi.org/10.1109/TAC.2025.3613909
Publication status	E-pub ahead of print - 24 Sept 2025

Funding

This work has been supported by The MathWorks Inc. and by the European Union within the framework of the National Laboratory for Autonomous Systems (RRF-2.3.1-21-2022-00002). Opinions, findings, conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the MathWorks Inc. or the European Union.

Keywords

Behavioral systems theory
data-driven simulation and control
linear parameter-varying systems

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10.1109/TAC.2025.3613909

Cite this

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title = "A behavioral approach for LPV data-driven representations",

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.",

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AU - Verhoek, Chris

AU - Markovsky, Ivan

AU - Haesaert, Sofie

AU - Tóth, Roland

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N2 - 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.

AB - 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.

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A behavioral approach for LPV data-driven representations

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