6 The Loewner framework for system identification and reduction

Karachalios, Dimitrios S.; Gosea, Ion Victor

doi:10.1515/9783110498967-006

Cited by 18 publications

(14 citation statements)

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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

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“…are evaluated at different frequencies to obtain frequency response data of the desired transfer function, then a MIMO system identification is performed based on the Loewner method [36][37][38]. Low-order models (about 50 states) are obtained by truncating the data and considering only frequencies lower than 5 Hz.…”

Section: A Aeroelastic Modelmentioning

confidence: 99%

Robust Gust Load Alleviation at Different Flight Points and Mass configurations

Fournier

Massioni

Pham

et al. 2022

AIAA SCITECH 2022 Forum

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This work studies the gust load alleviation of a flexible aircraft equipped with a lidar sensor that measures the wind velocity ahead of the aircraft. The focus is put on the aeroelastic dynamics uncertainties due to the evolution of the velocity and the altitude during a flight, and to the variations of the aircraft mass configuration. A robust control approach is adopted in order to minimize the aircraft loads due to the wind in presence of such uncertainties with low-order controllers that satisfy the constraints imposed by the system's limitations and the implementability considerations. This is achieved through structured mixed H 2 /H ∞ synthesis with multiple models. The load alleviation capability of controllers of various orders, using a variable number of control surfaces, is assessed through the computation of the maximum loads obtained in various conditions of velocity, altitude and mass configurations.

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“…We compare our proposed approach, where we carefully choose measurement points, with the Loewner approach, where logarithmically equidistant measurement points are considered. In both cases, we choose the best splitting method of right and left interpolation points as discussed in Karachalios et al (2020). In the following, we also note some details.…”

Section: Numerical Experimentsmentioning

confidence: 99%

A greedy data collection scheme for linear dynamical systems

Cherifi

Goyal

Benner

2022

DCE

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Mathematical models are essential to analyze and understand the dynamics of complex systems. Recently, data-driven methodologies have gotten a lot of attention which is leveraged by advancements in sensor technology. However, the quality of obtained data plays a vital role in learning a good and reliable model. Therefore, in this paper, we propose an efficient heuristic methodology to collect data both in the frequency domain and the time domain, aiming at having more information gained from limited experimental data than equidistant points. In the frequency domain, the interpolation points are restricted to the imaginary axis as the transfer function can be estimated easily on the imaginary axis. The efficiency of the proposed methodology is illustrated by means of several examples, and its robustness in the presence of noisy data is shown.

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6 The Loewner framework for system identification and reduction

Cited by 18 publications

References 0 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

Robust Gust Load Alleviation at Different Flight Points and Mass configurations

A greedy data collection scheme for linear dynamical systems

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