The Loewner framework for nonlinear identification and reduction of Hammerstein cascaded dynamical systems

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

doi:10.1002/pamm.202000337

Cited by 4 publications

(11 citation statements)

References 5 publications

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“…Recall the partitioning of the sampling points in (18). In Theorem 1, we have shown that r 2 (s, z) interpolates H 2 (s, z) over the sampling set ξ × ξ.…”

Section: Barycentric Representations For Lqo Systemsmentioning

confidence: 96%

“…Then, the goal is to a construct a data-driven LQO system directly from its samples without access access to internal dynamics of Σ LQO . The partition (18) and the error measure used in approximating the data will be clarified later. First we will show how the data in ( 16) and ( 17) can be used to develop barycentric-like representations corresponding to a reduced LQO system.…”

Section: Barycentric Representations For Lqo Systemsmentioning

confidence: 99%

“…Lemma 2. Let r 2 (s, z) be as defined in (28) corresponding to the sampling points in (18) and the data in (17). Then,…”

Section: Barycentric Representations For Lqo Systemsmentioning

confidence: 99%

“…Nevertheless, the methods previously mentioned are based in the time domain, while in this paper we focus on frequency domain data. We point out that the frequency-data based Loewner framework was recently extended to identifying Hammer-stein models in [18].…”

Section: Introductionmentioning

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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“…Recall the partitioning of the sampling points in (18). In Theorem 1, we have shown that r 2 (s, z) interpolates H 2 (s, z) over the sampling set ξ × ξ.…”

Section: Barycentric Representations For Lqo Systemsmentioning

confidence: 96%

Section: Barycentric Representations For Lqo Systemsmentioning

confidence: 99%

“…Lemma 2. Let r 2 (s, z) be as defined in (28) corresponding to the sampling points in (18) and the data in (17). Then,…”

Section: Barycentric Representations For Lqo Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Gosea¹,

Gugercin²

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Introductionmentioning

confidence: 99%

Data-Driven Modeling of Linear Dynamical Systems with Quadratic Output in the AAA Framework

Gosea

Gugercin

2022

J Sci Comput

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We extend the Adaptive Antoulas-Anderson () algorithm to develop a data-driven modeling framework for linear systems with quadratic output (). 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 systems. This analysis leads to the proposed 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 models. Two numerical test cases illustrate the efficiency of the proposed method.

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Research on Identification Algorithm of Cascade Control System

Ding

Wang

Zhang

et al. 2022

Mathematical Problems in Engineering

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Aiming at the problem of object model identification of modern industrial process control systems, a new closed-loop moment parameter identification online method based on the data of normal operation of the running system is proposed. In this method, only one step response data of the system is required, and appropriate convergence factors are introduced into the Laplace formula, the trapezoidal integral method is used to calculate the values of two derivatives of the transfer function, then the four unknown parameters of the second-order model can be solved by fitting the data with the least square method, and the target model can be identified. Finally, the simulation results of building different objects through Matlab show that the identification method has general applicability and good robustness with high recognition, and it is not sensitive to noise signals.

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The Loewner framework for nonlinear identification and reduction of Hammerstein cascaded dynamical systems

Cited by 4 publications

References 5 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

Data-Driven Modeling of Linear Dynamical Systems with Quadratic Output in the AAA Framework

Research on Identification Algorithm of Cascade Control System

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