2021
DOI: 10.1007/978-3-030-72983-7_1
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On Bilinear Time-Domain Identification and Reduction in the Loewner Framework

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Cited by 12 publications
(10 citation statements)
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“…As it is shown in Lemma 1, this could be achieved by exciting the system (as a black box) with purely oscillatory control inputs and measuring the outputs, and performing a Fourier transformation. For more details on such procedures in similar settings, we refer the reader to [17]. We also note that [27] examines systems described by two time-domain kernels together with their Fourier transformations (deemed as transfer functions) and their measurements.…”
Section: The Transfer Functions Of Lqo Systemsmentioning
confidence: 99%
See 1 more Smart Citation
“…As it is shown in Lemma 1, this could be achieved by exciting the system (as a black box) with purely oscillatory control inputs and measuring the outputs, and performing a Fourier transformation. For more details on such procedures in similar settings, we refer the reader to [17]. We also note that [27] examines systems described by two time-domain kernels together with their Fourier transformations (deemed as transfer functions) and their measurements.…”
Section: The Transfer Functions Of Lqo Systemsmentioning
confidence: 99%
“…Assume the set-up in Proposition 1. Further assume that the H 2 (s, z) samples in (17) are given. Define, the two-variable function r 2 (s, z) in a barycentric-like form:…”
Section: Barycentric Representations For Lqo Systemsmentioning
confidence: 99%
“…As seen in the sequel, this is by no means restrictive. In recent years, many data-driven and learning methods have been designed specifically for the case of BTIs [20,21] and also for QBTIs [22][23][24][25][26]. Here, we mention another prolific method for learning models from data, the so-called dynamic mode decomposition (DMD) [27,28], which was recently extended to deal with BTIs in [29,30].…”
Section: Introductionmentioning
confidence: 99%
“…The method proposed in this work comes as a continuation of [14], and represents an extension of the case with bilinear nonlinearities treated in [16]. It is a non-intrusive method in the sense that we do not require access to the system's matrices.…”
Section: Introductionmentioning
confidence: 99%
“…Afterwards, we propose an iterative algorithm that solves a linearized LS coupled problem (by taking into account all data). Different than earlier methods such as [14,16], in this paper we propose an adaptive iterative scheme for learning reduced-order models based on fitting input-output data corresponding to higher-order harmonics. We also take into account noisy data, in the sense that the measurements can be assumed to be corrupted by noise.…”
Section: Introductionmentioning
confidence: 99%