{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/30139"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/30139","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Methods of Computing Functional Gains for LQR Control of Partial Differential Equations","abstract":"This work focuses on a comparison of numerical methods for linear quadratic regulator (LQR) problems defined by parabolic partial differential equations. In particular, we study various methods for computing functional gains to boundary control problems for the heat equation. These methods require us to solve various equations including the algebraic Riccati equation, the Riccati partial differential equation and the Chandrasekhar partial differential equations. Numerical results are presented for control of a one-dimensional and a two-dimensional heat equation with Dirichlet or Robin boundary control.","abstract_html":"This work focuses on a comparison of numerical methods for linear quadratic regulator (LQR) problems defined by parabolic partial differential equations. In particular, we study various methods for computing functional gains to boundary control problems for the heat equation. These methods require us to solve various equations including the algebraic Riccati equation, the Riccati partial differential equation and the Chandrasekhar partial differential equations. Numerical results are presented for control of a one-dimensional and a two-dimensional heat equation with Dirichlet or Robin boundary control.","abstract_has_math":false,"creators":["Hulsing, Kevin P."],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Mathematics","degree_department":"Mathematics","school":null,"contributors":[],"advisors":[],"committee_chairs":["Burns, John A."],"committee_members":["Herdman, Terry L.","Cliff, Eugene M.","Borggaard, Jeffrey T.","King, Belinda B."],"year":1999,"date_issued":"1999-10-12","date_published":"1999-10-12","updated_at":"2026-07-22T22:20:05Z","subjects":["Riccati equations","Chandrasekhar equations","boundary control","heat equation","LQR problem"],"languages":[],"rights":["In Copyright"],"rights_urls":["http://rightsstatements.org/vocab/InC/1.0/"],"identifier_entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-121799-163931"],"render_values":[{"text":"etd-121799-163931","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/10919/30139","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.committeechair","label":"Committee Chair","values":["Burns, John A."]},{"key":"dc:contributor.committeemember","label":"Committee Member","values":["Herdman, Terry L.","Cliff, Eugene M.","Borggaard, Jeffrey T.","King, Belinda B."]},{"key":"dc:contributor.department","label":"Department","values":["Mathematics"]},{"key":"dc:creator","label":"Author","values":["Hulsing, Kevin P."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-14T20:20:49Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-14T20:20:49Z","2001-01-09"]},{"key":"dc:date.issued","label":"Date","values":["1999-10-12"]},{"key":"dc:publisher","label":"Institution","values":["Virginia Tech"]},{"key":"dc:type","label":"Dc Type","values":["Dissertation"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["doctoral"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph. D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Virginia Polytechnic Institute and State University"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Riccati equations","Chandrasekhar equations","boundary control","heat equation","LQR problem"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["In Copyright"]},{"key":"dc:rights.uri","label":"Rights URI","values":["http://rightsstatements.org/vocab/InC/1.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.other","label":"Dc Identifier Other","values":["etd-121799-163931"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/10919/30139"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This work focuses on a comparison of numerical methods for linear quadratic regulator (LQR) problems defined by parabolic partial differential equations. In particular, we study various methods for computing functional gains to boundary control problems for the heat equation. These methods require us to solve various equations including the algebraic Riccati equation, the Riccati partial differential equation and the Chandrasekhar partial differential equations. Numerical results are presented for control of a one-dimensional and a two-dimensional heat equation with Dirichlet or Robin boundary control."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:title","label":"Title","values":["Methods of Computing Functional Gains for LQR Control of Partial Differential Equations"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Burns, John A."],"dc:contributor.committeemember":["Herdman, Terry L.","Cliff, Eugene M.","Borggaard, Jeffrey T.","King, Belinda B."],"dc:contributor.department":["Mathematics"],"dc:creator":["Hulsing, Kevin P."],"dc:date.accessioned":["2014-03-14T20:20:49Z"],"dc:date.available":["2014-03-14T20:20:49Z","2001-01-09"],"dc:date.issued":["1999-10-12"],"dc:description.abstract":["This work focuses on a comparison of numerical methods for linear quadratic regulator (LQR) problems defined by parabolic partial differential equations. In particular, we study various methods for computing functional gains to boundary control problems for the heat equation. These methods require us to solve various equations including the algebraic Riccati equation, the Riccati partial differential equation and the Chandrasekhar partial differential equations. Numerical results are presented for control of a one-dimensional and a two-dimensional heat equation with Dirichlet or Robin boundary control."],"dc:description.degree":["Ph. D."],"dc:identifier.other":["etd-121799-163931"],"dc:identifier.uri":["http://hdl.handle.net/10919/30139"],"dc:publisher":["Virginia Tech"],"dc:rights":["In Copyright"],"dc:rights.uri":["http://rightsstatements.org/vocab/InC/1.0/"],"dc:subject":["Riccati equations","Chandrasekhar equations","boundary control","heat equation","LQR problem"],"dc:title":["Methods of Computing Functional Gains for LQR Control of Partial Differential Equations"],"dc:type":["Dissertation"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["doctoral"],"thesis:degree_name":["Ph. D."],"thesis:institution_name":["Virginia Polytechnic Institute and State University"]},"updated_at":"2026-07-22T22:20:05Z"}