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arXiv · 2412.18543

A behavioral approach for LPV data-driven representations

Chris Verhoek·Ivan Markovsky·Sofie Haesaert·Roland Tóth
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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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Chris Verhoek, Ivan Markovsky, Sofie Haesaert, Roland Tóth. 2024-12-24. A behavioral approach for LPV data-driven representations. https://doi.org/10.1109/tac.2025.3613909

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