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dc.contributor.authorHu, Weiweien_US
dc.date.accessioned2014-03-14T21:15:11Z
dc.date.available2014-03-14T21:15:11Z
dc.date.issued2012-05-21en_US
dc.identifier.otheretd-06192012-174604en_US
dc.identifier.urihttp://hdl.handle.net/10919/38664
dc.description.abstractIn this thesis we present theoretical and numerical results for a feedback control problem defined by a thermal fluid. The problem is motivated by recent interest in designing and controlling energy efficient building systems. In particular, we show that it is possible to locally exponentially stabilize the nonlinear Boussinesq Equations by applying Neumann/Robin type boundary control on a bounded and connected domain. The feedback controller is obtained by solving a Linear Quadratic Regulator problem for the linearized Boussinesq equations. Applying classical results for semilinear equations where the linear term generates an analytic semigroup, we establish that this Riccati-based optimal boundary feedback control provides a local stabilizing controller for the full nonlinear Boussinesq equations. In addition, we present a finite element Galerkin approximation. Finally, we provide numerical results based on standard Taylor-Hood elements to illustrate the theory.en_US
dc.publisherVirginia Techen_US
dc.relation.haspartHu_WW_D_2012.pdfen_US
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to Virginia Tech or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectTaylor-Hood Elementsen_US
dc.subjectAnalytic Semigroupen_US
dc.subjectAlgebraic Riccati Equationen_US
dc.subjectLQR Controlen_US
dc.subjectBoundary Feedback Controlen_US
dc.subjectBoussinesq Equationsen_US
dc.titleApproximation and Control of the Boussinesq Equations with Application to Control of Energy Efficient Building Systemsen_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairBurns, John A.en_US
dc.contributor.committeememberCliff, Eugene M.en_US
dc.contributor.committeememberZietsman, Lizetteen_US
dc.contributor.committeememberBall, Joseph A.en_US
dc.contributor.committeememberBorggaard, Jeffrey T.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06192012-174604/en_US
dc.date.sdate2012-06-19en_US
dc.date.rdate2012-07-16
dc.date.adate2012-07-16en_US


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