On Bilinear Time-Domain Identification and Reduction in the Loewner Framework

Karachalios, Dimitrios S.; Gosea, Ion Victor; Antoulas, Athanasios C.

doi:10.1007/978-3-030-72983-7_1

Cited by 12 publications

(10 citation statements)

References 30 publications

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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%

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Data-driven modeling of linear dynamical systems with quadratic output in the AAA framework

Gosea¹,

Gugercin²

2021

Preprint

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We extend the AAA (Adaptive-Antoulas-Anderson) algorithm to develop a data-driven modeling framework for linear systems with quadratic output (LQO). Such systems are characterized by two transfer functions: one corresponding to the linear part of the output and another one to the quadratic part. We first establish the joint barycentric representations and the interpolation theory for the two transfer functions of LQO systems. This analysis leads to the proposed AAA-LQO algorithm. We show that by interpolating the transfer function values on a subset of samples together with imposing a least-squares minimization on the rest, we construct reliable data-driven LQO models. Two numerical test cases illustrate the efficiency of the proposed method.

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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%

Data-driven modeling of linear dynamical systems with quadratic output in the AAA framework

Gosea¹,

Gugercin²

2021

Preprint

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“…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%

Exact and Inexact Lifting Transformations of Nonlinear Dynamical Systems: Transfer Functions, Equivalence, and Complexity Reduction

Gosea

2022

Applied Sciences

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In this work, we deal with the problem of approximating and equivalently formulating generic nonlinear systems by means of specific classes thereof. Bilinear and quadratic-bilinear systems accomplish precisely this goal. Hence, by means of exact and inexact lifting transformations, we are able to reformulate the original nonlinear dynamics into a different, more simplified format. Additionally, we study the problem of complexity/model reduction of large-scale lifted models of nonlinear systems from data. The method under consideration is the Loewner framework, an established data-driven approach that requires samples of input–output mappings. The latter are known as generalized transfer functions, which are appropriately defined for both bilinear and quadratic-bilinear systems. We show connections between these mappings as well as between the matrices of reduced-order models. Finally, we illustrate the theoretical discussion with two numerical examples.

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“…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%

Learning reduced-order models of quadratic control systems from input-output data

Gosea,

Karachalios,

Antoulas

2020

Preprint

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In this paper, we address an extension of the Loewner framework for learning quadratic control systems from input-output data. The proposed method first constructs a reduced-order linear model from measurements of the classical transfer function. Then, this surrogate model is enhanced by incorporating a term that depends quadratically on the state. More precisely, we employ an iterative procedure based on least squares fitting that takes into account measured or computed data. Here, data represent transfer function values inferred from higher harmonics of the observed output, when the control input is purely oscillatory.

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On Bilinear Time-Domain Identification and Reduction in the Loewner Framework

Cited by 12 publications

References 30 publications

Data-driven modeling of linear dynamical systems with quadratic output in the AAA framework

Data-driven modeling of linear dynamical systems with quadratic output in the AAA framework

Exact and Inexact Lifting Transformations of Nonlinear Dynamical Systems: Transfer Functions, Equivalence, and Complexity Reduction

Learning reduced-order models of quadratic control systems from input-output data

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