A greedy data collection scheme for linear dynamical systems

Cherifi, Karim; Goyal, Pawan; Benner, Peter

doi:10.1017/dce.2022.16

Cited by 7 publications

(1 citation statement)

References 33 publications

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“…Finally, it is to be noted that the choice of interpolation points is crucial in the LF. An exhaustive study of different choices was proposed in [37], while a greedy strategy was proposed in [17], for scenarios in which limited experimental data are available.…”

Section: The Loewner Framework Inmentioning

confidence: 99%

Practical challenges in data-driven interpolation: dealing with noise, enforcing stability, and computing realizations

Aumann¹,

Gosea²

2023

Preprint

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In this contribution, we propose a detailed study of interpolation-based datadriven methods that are of relevance in the model reduction and also in the systems and control communities. The data are given by samples of the transfer function of the underlying (unknown) model, i.e., we analyze frequency-response data. We also propose novel approaches that combine some of the main attributes of the established methods, for addressing particular issues. This includes placing poles and hence, enforcing stability of reduced-order models, robustness to noisy or perturbed data, and switching from different rational function representations. We mention here the classical state-space format and also various barycentric representations of the fitted rational interpolants. We show that the newly-developed approaches yield, in some cases, superior numerical results, when comparing to the established methods. The numerical results include a thorough analysis of various aspects related to approximation errors, choice of interpolation points, or placing dominant poles, which are tested on some benchmark models and data-sets.

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Section: The Loewner Framework Inmentioning

confidence: 99%

Practical challenges in data-driven interpolation: dealing with noise, enforcing stability, and computing realizations

Aumann¹,

Gosea²

2023

Preprint

View full text Add to dashboard Cite

show abstract

Practical challenges in data‐driven interpolation: Dealing with noise, enforcing stability, and computing realizations

Aumann,

Gosea

2023

Adaptive Control & Signal

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SummaryIn this contribution, we propose a detailed study of interpolation‐based data‐driven methods that are of relevance in the model reduction and also in the systems and control communities. The data are given by samples of the transfer function of the underlying (unknown) model, that is, we analyze frequency‐response data. We also propose novel approaches that combine some of the main attributes of the established methods, for addressing particular issues. This includes placing poles and hence, enforcing stability of reduced‐order models, robustness to noisy or perturbed data, and switching from different rational function representations. We mention here the classical state‐space format and also various barycentric representations of the fitted rational interpolants. We show that the newly‐developed approaches yield, in some cases, superior numerical results, when comparing to the established methods. The numerical results include a thorough analysis of various aspects related to approximation errors, choice of interpolation points, or placing dominant poles, which are tested on some benchmark models and data‐sets.

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Toward a certified greedy Loewner framework with minimal sampling

Pradovera

2023

Adv Comput Math

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We propose a strategy for greedy sampling in the context of non-intrusive interpolation-based surrogate modeling for frequency-domain problems. We rely on a non-intrusive and cheap error indicator to drive the adaptive selection of the high-fidelity samples on which the surrogate is based. We develop a theoretical framework to support our proposed indicator. We also present several practical approaches for the termination criterion that is used to end the greedy sampling iterations. To showcase our greedy strategy, we numerically test it in combination with the well-known Loewner framework. To this effect, we consider several benchmarks, highlighting the effectiveness of our adaptive approach in approximating the transfer function of complex systems from a few samples.

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A greedy data collection scheme for linear dynamical systems

Cited by 7 publications

References 33 publications

Practical challenges in data-driven interpolation: dealing with noise, enforcing stability, and computing realizations

Practical challenges in data-driven interpolation: dealing with noise, enforcing stability, and computing realizations

Practical challenges in data‐driven interpolation: Dealing with noise, enforcing stability, and computing realizations

Toward a certified greedy Loewner framework with minimal sampling

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