{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69414"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69414","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Performance and Robustness of Adaptive Controllers for Linear Stochastic Systems","abstract":"In this thesis we address the twin questions of performance as well as robustness of an adaptive controller for linear stochastic systems. Regarding the performance problem, we consider the issue of convergence of the parameter estimates with respect to the stochastic gradient algorithm and the modified least squares algorithm. As to the linear model following problem, we have shown that under certain conditions, both algorithms are strongly consistent. For the general tracking problem, if the reference trajectory is sufficiently rich of order greater than or equal to a certain positive number, both algorithms are strongly consistent. As for the regulation problem, if the controller utilizes the stochastic gradient algorithm, the parameter estimates converge to a random scalar multiple of the true parameter vector. For the robustness problem, we have presented a robust adaptive controller. Its mean square stabilizes the ideal system optimally if the noise signal satisfies a positive real condition. It can also stabilize a non-ideal system if the system is in a certain graph topological neighborhood of an ideal system.","abstract_html":"In this thesis we address the twin questions of performance as well as robustness of an adaptive controller for linear stochastic systems. Regarding the performance problem, we consider the issue of convergence of the parameter estimates with respect to the stochastic gradient algorithm and the modified least squares algorithm. As to the linear model following problem, we have shown that under certain conditions, both algorithms are strongly consistent. For the general tracking problem, if the reference trajectory is sufficiently rich of order greater than or equal to a certain positive number, both algorithms are strongly consistent. As for the regulation problem, if the controller utilizes the stochastic gradient algorithm, the parameter estimates converge to a random scalar multiple of the true parameter vector. For the robustness problem, we have presented a robust adaptive controller. Its mean square stabilizes the ideal system optimally if the noise signal satisfies a positive real condition. It can also stabilize a non-ideal system if the system is in a certain graph topological neighborhood of an ideal system.","abstract_has_math":false,"creators":["Lin, Sheng-Fuu"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":["Kumar, P.R."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-15T19:05:41Z","date_published":"2014-12-15T19:05:41Z","updated_at":"2026-07-22T22:26:00Z","subjects":["Engineering, Electronics and Electrical"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8908755"],"render_values":[{"text":"(UMI)AAI8908755","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69414","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kumar, P.R."]},{"key":"dc:creator","label":"Author","values":["Lin, Sheng-Fuu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T19:05:41Z","10000-01-01","1988"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering, Electronics and Electrical"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/69414","(UMI)AAI8908755"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis we address the twin questions of performance as well as robustness of an adaptive controller for linear stochastic systems. Regarding the performance problem, we consider the issue of convergence of the parameter estimates with respect to the stochastic gradient algorithm and the modified least squares algorithm. As to the linear model following problem, we have shown that under certain conditions, both algorithms are strongly consistent. For the general tracking problem, if the reference trajectory is sufficiently rich of order greater than or equal to a certain positive number, both algorithms are strongly consistent. As for the regulation problem, if the controller utilizes the stochastic gradient algorithm, the parameter estimates converge to a random scalar multiple of the true parameter vector. For the robustness problem, we have presented a robust adaptive controller. Its mean square stabilizes the ideal system optimally if the noise signal satisfies a positive real condition. It can also stabilize a non-ideal system if the system is in a certain graph topological neighborhood of an ideal system.","Made available in DSpace on 2014-12-15T19:05:41Z (GMT). No. of bitstreams: 1 8908755.pdf: 3107655 bytes, checksum: 92fbd54b4ffd7865b5a04302a9ff911d (MD5) Previous issue date: 1988","Embargo set by: Seth Robbins for item 69580 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","129 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1988."]},{"key":"dc:title","label":"Title","values":["Performance and Robustness of Adaptive Controllers for Linear Stochastic Systems"]}]}],"canonical_facts":{"dc:contributor":["Kumar, P.R."],"dc:creator":["Lin, Sheng-Fuu"],"dc:date":["2014-12-15T19:05:41Z","10000-01-01","1988"],"dc:description":["In this thesis we address the twin questions of performance as well as robustness of an adaptive controller for linear stochastic systems. Regarding the performance problem, we consider the issue of convergence of the parameter estimates with respect to the stochastic gradient algorithm and the modified least squares algorithm. As to the linear model following problem, we have shown that under certain conditions, both algorithms are strongly consistent. For the general tracking problem, if the reference trajectory is sufficiently rich of order greater than or equal to a certain positive number, both algorithms are strongly consistent. As for the regulation problem, if the controller utilizes the stochastic gradient algorithm, the parameter estimates converge to a random scalar multiple of the true parameter vector. For the robustness problem, we have presented a robust adaptive controller. Its mean square stabilizes the ideal system optimally if the noise signal satisfies a positive real condition. It can also stabilize a non-ideal system if the system is in a certain graph topological neighborhood of an ideal system.","Made available in DSpace on 2014-12-15T19:05:41Z (GMT). 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