On the Tightness of the Balanced Truncation Error Bound with an Application to Arrowhead Systems

Simple item page
dc.contributor.authorReiter, Sean Josephen
dc.contributor.committeechairEmbree, Mark P.en
dc.contributor.committeememberBeattie, Christopher A.en
dc.contributor.committeememberGugercin, Serkanen
dc.contributor.committeememberKekatos, Vasileiosen
dc.contributor.departmentMathematicsen
dc.date.accessioned2022-01-29T09:00:40Zen
dc.date.available2022-01-29T09:00:40Zen
dc.date.issued2022-01-28en
dc.description.abstractBalanced truncation model reduction for linear systems yields reduced-order models that satisfy a well-known error bound in terms of a system's Hankel singular values. This bound is known to hold with equality under certain conditions, such as when the full-order system is state-space symmetric. In this work, we derive more general conditions in which the balanced truncation error bound holds with equality. We show that this holds for single-input, single-output systems that exhibit a generalized type of state-space symmetry based on the sign parameters corresponding to a system's Hankel singular values. We prove an additional result that shows how to determine this state-space symmetry from the arrowhead realization of a system, if available. In particular, we provide a formula for the sign parameters of an arrowhead system in terms of the off-diagonal entries of its arrowhead realization. We then illustrate these results with an example of an arrowhead system arising naturally in power systems modeling that motivated our study.en
dc.description.abstractgeneralMathematical modeling of dynamical systems provides a powerful means for studying physical phenomena. Due the complexities of real-world problems, many mathematical models face computational difficulties due to the costs of accurate modeling. Model-order reduction of large-scale dynamical systems circumvents this by approximating the large-scale model with a ``smaller'' one that still accurately describes the problem of interest. Balanced truncation model reduction for linear systems is one such example, yielding reduced-order models that satisfy a tractable upper bound on the approximation error. This work investigates conditions in which this bound is known to hold with equality, becoming an exact formula for the error in reduction. We additionally show how to determine these conditions for a special class of linear dynamical systems known as arrowhead systems, which arise in special applications of network modeling. We provide an example of one such system from power systems modeling that motivated our study.en
dc.description.degreeMaster of Scienceen
dc.format.mediumETDen
dc.identifier.othervt_gsexam:33886en
dc.identifier.urihttp://hdl.handle.net/10919/107999en
dc.language.isoenen
dc.publisherVirginia Techen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectModel Reductionen
dc.subjectBalanced Truncationen
dc.subjectError Bounden
dc.subjectArrowhead Systemsen
dc.subjectPower Systemsen
dc.titleOn the Tightness of the Balanced Truncation Error Bound with an Application to Arrowhead Systemsen
dc.typeThesisen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.levelmastersen
thesis.degree.nameMaster of Scienceen

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Reiter_SJ_T_2022.pdf
Size:
337.92 KB
Format:
Adobe Portable Document Format
Download

Collections

Masters Theses