Parametrized model reduction based on semidefinite programming

Summary, in English

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.

• Författare: Aivar Sootla; Kin Cheong Sou; Anders Rantzer
• Avdelning/ar: Institutionen för reglerteknik; ELLIIT: the Linköping-Lund initiative on IT and mobile communication
• Publiceringsår: 2013
• Språk: Engelska
• Sidor: 2840-2844
• Publikation/Tidskrift/Serie: Automatica
• Volym: 49
• Issue: 9
• Länkar: http://dx.doi.org/10.1016/j.automatica.2013.05.022
• Dokumenttyp: Artikel i tidskrift
• Förlag: Pergamon Press Ltd.
• Ämne: Control Engineering
• Nyckelord: Model reduction; Parameter-dependent linear systems; Semidefinite; programming
• Status: Published
• Forskningsgrupp: LCCC
• ISBN/ISSN/Övrigt: ISSN: 0005-1098