Model Reduction Using Semidefinite Programming
(2009) Abstract
 In this thesis model reduction methods for linear time invariant systems are investigated. The reduced models are computed using semidefinite programming. Two ways of imposing the stability constraint are considered. However, both approaches add a positivity constraint to the program. The input to the algorithms is a number of frequency response samples of the original model. This makes the computational complexity relatively low for largescale models. Extra properties on a reduced model can also be enforced, as long as the properties can be expressed as convex conditions. Semidefinite program are solved using the interior point methods which are well developed, making the implementation simpler.
A number of extensions... (More)  In this thesis model reduction methods for linear time invariant systems are investigated. The reduced models are computed using semidefinite programming. Two ways of imposing the stability constraint are considered. However, both approaches add a positivity constraint to the program. The input to the algorithms is a number of frequency response samples of the original model. This makes the computational complexity relatively low for largescale models. Extra properties on a reduced model can also be enforced, as long as the properties can be expressed as convex conditions. Semidefinite program are solved using the interior point methods which are well developed, making the implementation simpler.
A number of extensions to the proposed methods were studied, for example, passive model reduction, frequencyweighted model reduction. An interesting extension is reduction of parameterized linear time invariant models, i.e. models with statespace matrices dependent on parameters. It is assumed, that parameters do not depend on state variables nor time. This extension is valuable in modeling, when a set of parameters has to be chosen to fit the required specifications. A good illustration of such a problem is modeling of a spiral radio frequency inductor. The physical model depends nonlinearly on two parameters: wire width and wire separation. To chose optimally both parameters a loworder model is usually created. The inductor modeling is considered as a case study in this thesis. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1624919
 author
 Sootla, Aivar ^{LU}
 supervisor

 Anders Rantzer ^{LU}
 organization
 publishing date
 2009
 type
 Thesis
 publication status
 published
 subject
 keywords
 semidefinite programming, model reduction, convex optimization
 publisher
 Department of Automatic Control, Lund Institute of Technology, Lund University
 language
 English
 LU publication?
 yes
 id
 ea565a77e364418aa5c75ab2150c2b93 (old id 1624919)
 date added to LUP
 20100629 08:56:23
 date last changed
 20160919 08:44:49
@misc{ea565a77e364418aa5c75ab2150c2b93, abstract = {In this thesis model reduction methods for linear time invariant systems are investigated. The reduced models are computed using semidefinite programming. Two ways of imposing the stability constraint are considered. However, both approaches add a positivity constraint to the program. The input to the algorithms is a number of frequency response samples of the original model. This makes the computational complexity relatively low for largescale models. Extra properties on a reduced model can also be enforced, as long as the properties can be expressed as convex conditions. Semidefinite program are solved using the interior point methods which are well developed, making the implementation simpler.<br/><br> <br/><br> A number of extensions to the proposed methods were studied, for example, passive model reduction, frequencyweighted model reduction. An interesting extension is reduction of parameterized linear time invariant models, i.e. models with statespace matrices dependent on parameters. It is assumed, that parameters do not depend on state variables nor time. This extension is valuable in modeling, when a set of parameters has to be chosen to fit the required specifications. A good illustration of such a problem is modeling of a spiral radio frequency inductor. The physical model depends nonlinearly on two parameters: wire width and wire separation. To chose optimally both parameters a loworder model is usually created. The inductor modeling is considered as a case study in this thesis.}, author = {Sootla, Aivar}, keyword = {semidefinite programming,model reduction,convex optimization}, language = {eng}, note = {Licentiate Thesis}, publisher = {Department of Automatic Control, Lund Institute of Technology, Lund University}, title = {Model Reduction Using Semidefinite Programming}, year = {2009}, }