An Interpolation-Based Approach to Optimal H∞ Model Reduction

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dc.contributor.authorFlagg, Garret Michaelen
dc.contributor.committeechairGugercin, Serkanen
dc.contributor.committeememberBeattie, Christopher A.en
dc.contributor.committeememberBorggaard, Jeffrey T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T20:38:17Zen
dc.date.adate2009-06-01en
dc.date.available2014-03-14T20:38:17Zen
dc.date.issued2009-05-05en
dc.date.rdate2009-06-01en
dc.date.sdate2009-05-22en
dc.description.abstractA model reduction technique that is optimal in the H<sub>∞</sub>-norm has long been pursued due to its theoretical and practical importance. We consider the optimal H<sub>∞</sub> model reduction problem broadly from an interpolation-based approach, and give a method for finding the approximation to a state-space symmetric dynamical system which is optimal over a family of interpolants to the full order system. This family of interpolants has a simple parameterization that simplifies a direct search for the optimal interpolant. Several numerical examples show that the interpolation points satisfying the Meier-Luenberger conditions for H₂-optimal approximations are a good starting point for minimizing the H<sub>∞</sub>-norm of the approximation error. Interpolation points satisfying the Meier-Luenberger conditions can be computed iteratively using the IRKA algorithm [12]. We consider the special case of state-space symmetric systems and show that simple sufficient conditions can be derived for minimizing the approximation error when starting from the interpolation points found by the IRKA algorithm. We then explore the relationship between potential theory in the complex plane and the optimal H<sub>∞</sub>-norm interpolation points through several numerical experiments. The results of these experiments suggest that the optimal H<sub>∞</sub> approximation of order r yields an error system for which significant pole-zero cancellation occurs, effectively reducing an order n+r error system to an order 2r+1 system. These observations lead to a heuristic method for choosing interpolation points that involves solving a rational Zolatarev problem over a discrete set of points in the complex plane.en
dc.description.degreeMaster of Scienceen
dc.identifier.otheretd-05222009-124513en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-05222009-124513/en
dc.identifier.urihttp://hdl.handle.net/10919/33123en
dc.publisherVirginia Techen
dc.relation.haspartmastersthesis.pdfen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectModel Reductionen
dc.subjectRational Interpolationen
dc.subjectOptimizationen
dc.titleAn Interpolation-Based Approach to Optimal H<sub>∞</sub> Model Reductionen
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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