Interpolation Methods for the Model Reduction of Bilinear Systems

Simple item page
dc.contributor.authorFlagg, Garret Michaelen
dc.contributor.committeechairGugercin, Serkanen
dc.contributor.committeememberBeattie, Christopher A.en
dc.contributor.committeememberBall, Joseph A.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:11:31Zen
dc.date.adate2012-05-31en
dc.date.available2014-03-14T20:11:31Zen
dc.date.issued2012-04-30en
dc.date.rdate2012-05-31en
dc.date.sdate2012-05-03en
dc.description.abstractBilinear systems are a class of nonlinear dynamical systems that arise in a variety of applications. In order to obtain a sufficiently accurate representation of the underlying physical phenomenon, these models frequently have state-spaces of very large dimension, resulting in the need for model reduction. In this work, we introduce two new methods for the model reduction of bilinear systems in an interpolation framework. Our first approach is to construct reduced models that satisfy multipoint interpolation constraints defined on the Volterra kernels of the full model. We show that this approach can be used to develop an asymptotically optimal solution to the H_2 model reduction problem for bilinear systems. In our second approach, we construct a solution to a bilinear system realization problem posed in terms of constructing a bilinear realization whose kth-order transfer functions satisfy interpolation conditions in k complex variables. The solution to this realization problem can be used to construct a bilinear system realization directly from sampling data on the kth-order transfer functions, without requiring the formation of the realization matrices for the full bilinear system.en
dc.description.degreePh. D.en
dc.identifier.otheretd-05032012-141857en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05032012-141857/en
dc.identifier.urihttp://hdl.handle.net/10919/27521en
dc.publisherVirginia Techen
dc.relation.haspartFlagg_GM_D_2012.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectOptimizationen
dc.subjectModel Reductionen
dc.subjectNonlinear systemsen
dc.subjectInterpolation theoryen
dc.subjectRational Krylov subspace methodsen
dc.titleInterpolation Methods for the Model Reduction of Bilinear Systemsen
dc.typeDissertationen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Flagg_GM_D_2012.pdf
Size:
1.36 MB
Format:
Adobe Portable Document Format
Download

Collections

Doctoral Dissertations