Parametrized model reduction based on semidefinite programming
Sootla, Aivar ; Sou, Kin Cheong and Rantzer, Anders LU
(2013)
In Automatica
49(9).
p.2840-2844
- Abstract
- A parametrized model in addition to the control and state-space variables depends on time-independent design parameters, which essentially define a family of models. The goal of parametrized model reduction is to approximate this family of models. In this paper, a reduction method for linear time-invariant (LTI) parametrized models is presented, which constitutes the development of a recently proposed reduction approach. Reduced order models are computed based on the finite number of frequency response samples of the full order model. This method uses a semidefinite relaxation, while enforcing stability on the reduced order model for all values of parameters of interest. As a main theoretical statement, the relaxation gap (the ratio... (More)
- A parametrized model in addition to the control and state-space variables depends on time-independent design parameters, which essentially define a family of models. The goal of parametrized model reduction is to approximate this family of models. In this paper, a reduction method for linear time-invariant (LTI) parametrized models is presented, which constitutes the development of a recently proposed reduction approach. Reduced order models are computed based on the finite number of frequency response samples of the full order model. This method uses a semidefinite relaxation, while enforcing stability on the reduced order model for all values of parameters of interest. As a main theoretical statement, the relaxation gap (the ratio between upper and lower bounds) is derived, which validates the relaxation. The proposed method is flexible in adding extra constraints (e.g., passivity can be enforced on reduced order models) and modifying the objective function (e.g., frequency weights can be added to the minimization criterion). The performance of the method is validated on a numerical example. (C) 2013 Elsevier Ltd. All rights reserved. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/4062764
- author
- Sootla, Aivar
; Sou, Kin Cheong
and Rantzer, Anders
LU
- organization
- publishing date
- 2013
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- Model reduction, Parameter-dependent linear systems, Semidefinite, programming
- in
- Automatica
- volume
- 49
- issue
- 9
- pages
- 2840 - 2844
- publisher
- Pergamon Press Ltd.
- external identifiers
-
- wos:000323594200029
- scopus:84881481808
- ISSN
- 0005-1098
- DOI
- 10.1016/j.automatica.2013.05.022
- language
- English
- LU publication?
- yes
- id
- 74a8ae21-e3f7-4e40-84ef-998e4f3f3388 (old id 4062764)
- date added to LUP
- 2016-04-01 15:05:54
- date last changed
- 2024-01-10 12:58:12
@article{74a8ae21-e3f7-4e40-84ef-998e4f3f3388,
abstract = {{A parametrized model in addition to the control and state-space variables depends on time-independent design parameters, which essentially define a family of models. The goal of parametrized model reduction is to approximate this family of models. In this paper, a reduction method for linear time-invariant (LTI) parametrized models is presented, which constitutes the development of a recently proposed reduction approach. Reduced order models are computed based on the finite number of frequency response samples of the full order model. This method uses a semidefinite relaxation, while enforcing stability on the reduced order model for all values of parameters of interest. As a main theoretical statement, the relaxation gap (the ratio between upper and lower bounds) is derived, which validates the relaxation. The proposed method is flexible in adding extra constraints (e.g., passivity can be enforced on reduced order models) and modifying the objective function (e.g., frequency weights can be added to the minimization criterion). The performance of the method is validated on a numerical example. (C) 2013 Elsevier Ltd. All rights reserved.}},
author = {{Sootla, Aivar and Sou, Kin Cheong and Rantzer, Anders}},
issn = {{0005-1098}},
keywords = {{Model reduction; Parameter-dependent linear systems; Semidefinite; programming}},
language = {{eng}},
number = {{9}},
pages = {{2840--2844}},
publisher = {{Pergamon Press Ltd.}},
series = {{Automatica}},
title = {{Parametrized model reduction based on semidefinite programming}},
url = {{http://dx.doi.org/10.1016/j.automatica.2013.05.022}},
doi = {{10.1016/j.automatica.2013.05.022}},
volume = {{49}},
year = {{2013}},
}