An interpolation-based approach to the weighted H2 model reduction problem

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dc.contributor.authorAnic, Branimiren
dc.contributor.committeechairGugercin, Serkanen
dc.contributor.committeememberBeattie, Christopher A.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:44:16Zen
dc.date.adate2008-10-10en
dc.date.available2014-03-14T20:44:16Zen
dc.date.issued2008-08-25en
dc.date.rdate2008-10-10en
dc.date.sdate2008-08-26en
dc.description.abstractDynamical systems and their numerical simulation are very important for investigating physical and technical problems. The more accuracy is desired, the more equations are needed to reach the desired level of accuracy. This leads to large-scale dynamical systems. The problem is that computations become infeasible due to the limitations on time and/or memory in large-scale settings. Another important issue is numerical ill-conditioning. These are the main reasons for the need of model reduction, i.e. replacing the original system by a reduced system of much smaller dimension. Then one uses the reduced models in order to simulate or control processes. The main goal of this thesis is to investigate an interpolation-based approach to the weighted-H2 model reduction problem. Nonetheless, first we will discuss the regular (unweighted) H2 model reduction problem. We will re-visit the interpolation conditions for H2-optimality, also known as Meier-Luenberger conditions, and discuss how to obtain an optimal reduced order system via projection. After having introduced the H2-norm and the unweighted-H2 model reduction problem, we will introduce the weighted-H2 model reduction problem. We will first derive a new error expression for the weighted-H2 model reduction problem. This error expression illustrates the significance of interpolation at the mirror images of the reduced system poles and the original system poles, as in the unweighted case. However, in the weighted case this expression yields that interpolation at the mirror images of the poles of the weighting system is also significant. Finally, based on the new weighted-H2 error expression, we will propose an iteratively corrected interpolation-based algorithm for the weighted-H2 model reduction problem. Moreover we will present new optimality conditions for the weighted-H2 approximation. These conditions occur as structured orthogonality conditions similar to those for the unweighted case which were derived by Antoulas, Beattie and Gugercin. We present several numerical examples to illustrate the effectiveness of the proposed approach and compare it with the frequency-weighted balanced truncation method. We observe that, for virtually all of our numerical examples, the proposed method outperforms the frequency-weighted balanced truncation method.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-08262008-135741en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-08262008-135741/en
dc.identifier.urihttp://hdl.handle.net/10919/34782en
dc.publisherVirginia Techen
dc.relation.haspartThesis_Branimir_Final.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectRational Kryloven
dc.subjectinterpolationen
dc.subjectH2 Approximationen
dc.subjectmodel reductionen
dc.titleAn interpolation-based approach to the weighted H2 model reduction problemen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

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