{"id":{"repo_id":"tdl","oai_identifier":"oai:tdl-ir.tdl.org:2346/58469"},"canonical_url":"https://search.dev.ndltd.org/etd/tdl/oai:tdl-ir.tdl.org:2346/58469","repository":{"repo_id":"tdl","name":"Texas Digital Library","base_url":"https://tdl-ir.tdl.org/server/oai/request"},"display":{"title":"Error analysis for harmonic tracking algorithm using geometric control","abstract":"Geometric Control Theory was initiated in the beginning of the 1970's and has now became a well established approach in addressing problems of tracking and disturbance rejections of time independent and dependent signals. This thesis describes the error analysis for time-dependent harmonic signal tracking in a particular control system using geometric controls. Here, we first discuss the basic setup and assumptions made in formulating the iterative scheme algorithm in geometric control. Next we present the main theorem of our work which bounds the norm of the error e(t) at each step when time tends to infinity. The aforementioned theorem was postulated as the consequence of two lemmas we proved during the study. Finally we illustrate this error estimate for harmonic tracking in one and two dimensional systems by numerically solving this control system using the finite element package "COMSOL".","abstract_html":"Geometric Control Theory was initiated in the beginning of the 1970's and has now became a well established approach in addressing problems of tracking and disturbance rejections of time independent and dependent signals. This thesis describes the error analysis for time-dependent harmonic signal tracking in a particular control system using geometric controls. Here, we first discuss the basic setup and assumptions made in formulating the iterative scheme algorithm in geometric control. Next we present the main theorem of our work which bounds the norm of the error e(t) at each step when time tends to infinity. The aforementioned theorem was postulated as the consequence of two lemmas we proved during the study. Finally we illustrate this error estimate for harmonic tracking in one and two dimensional systems by numerically solving this control system using the finite element package "COMSOL".","abstract_has_math":false,"creators":["Pathiranage, Thanuka W."],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Hoang, Luan T.","Aulisa, Eugenio","Gilliam, David S."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013-12","date_published":"2013-12","updated_at":"2026-07-27T21:19:21Z","subjects":["Error analysis","Harmonic tracking","Geometric controls","Error estimates"],"languages":["eng"],"rights":["Unrestricted."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2346/58469"],"render_values":[{"text":"http://hdl.handle.net/2346/58469","href":"http://hdl.handle.net/2346/58469","code":true}]}]},"links":{"outbound_url":"https://hdl.handle.net/2346/58469","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hoang, Luan T.","Aulisa, Eugenio","Gilliam, David S."]},{"key":"dc:creator","label":"Author","values":["Pathiranage, Thanuka W."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-03-23T22:28:25Z","2026-02-19T18:27:30Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-03-23T22:28:25Z"]},{"key":"dc:date.issued","label":"Date","values":["2013-12"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Error analysis","Harmonic tracking","Geometric controls","Error estimates"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Unrestricted."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2346/58469"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/2346/58469"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Geometric Control Theory was initiated in the beginning of the 1970's and has now became a well established approach in addressing problems of tracking and disturbance rejections of time independent and dependent signals. This thesis describes the error analysis for time-dependent harmonic signal tracking in a particular control system using geometric controls. Here, we first discuss the basic setup and assumptions made in formulating the iterative scheme algorithm in geometric control. Next we present the main theorem of our work which bounds the norm of the error e(t) at each step when time tends to infinity. The aforementioned theorem was postulated as the consequence of two lemmas we proved during the study. Finally we illustrate this error estimate for harmonic tracking in one and two dimensional systems by numerically solving this control system using the finite element package "COMSOL"."]},{"key":"dc:title","label":"Title","values":["Error analysis for harmonic tracking algorithm using geometric control"]}]}],"canonical_facts":{"dc:contributor":["Hoang, Luan T.","Aulisa, Eugenio","Gilliam, David S."],"dc:creator":["Pathiranage, Thanuka W."],"dc:date.accessioned":["2014-03-23T22:28:25Z","2026-02-19T18:27:30Z"],"dc:date.available":["2014-03-23T22:28:25Z"],"dc:date.issued":["2013-12"],"dc:description.abstract":["Geometric Control Theory was initiated in the beginning of the 1970's and has now became a well established approach in addressing problems of tracking and disturbance rejections of time independent and dependent signals. This thesis describes the error analysis for time-dependent harmonic signal tracking in a particular control system using geometric controls. Here, we first discuss the basic setup and assumptions made in formulating the iterative scheme algorithm in geometric control. Next we present the main theorem of our work which bounds the norm of the error e(t) at each step when time tends to infinity. The aforementioned theorem was postulated as the consequence of two lemmas we proved during the study. Finally we illustrate this error estimate for harmonic tracking in one and two dimensional systems by numerically solving this control system using the finite element package "COMSOL"."],"dc:identifier":["http://hdl.handle.net/2346/58469"],"dc:identifier.uri":["https://hdl.handle.net/2346/58469"],"dc:language":["eng"],"dc:rights":["Unrestricted."],"dc:subject":["Error analysis","Harmonic tracking","Geometric controls","Error estimates"],"dc:title":["Error analysis for harmonic tracking algorithm using geometric control"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T21:19:21Z"}