Data-driven modeling with prior system knowledge

The behavior of a linear time-invariant system can be characterized entirely by measured input–output data that spans the vector space of all possible trajectories of the system relying on the fundamental lemma by Willems et al. However, useful a priori knowledge of the system is usually neglected. We propose a novel method for incorporating prior knowledge, specifically, known pole and zero locations, into a data-driven representation by constructing filters that pre-process the measured input–output data. To this end, a physics-informed data-driven predictor is introduced, where trajectories are obtained as linear combinations of the columns of a filtered block-Hankel matrix. We explicitly derive the output prediction error and show how leveraging prior knowledge reduces the impact of future noise realizations on output predictions and improves the accuracy of the initial state that is inferred from past data.

Subjects

Data-driven control

Filtering

Persistency of excitation

Physics-informed learning

System identification

DDC Class

629.8: Control and Feedback Control Systems

519: Applied Mathematics, Probabilities

006.3: Artificial Intelligence

Lizenz

https://creativecommons.org/licenses/by/4.0/

Publication version

publishedVersion

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1-s2.0-S2468601826000246-main.pdf

Type

Main Article

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529.06 KB

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Adobe PDF

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Data-driven modeling with prior system knowledge