{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/69348"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/69348","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Integral Manifolds of Slow Adaptation (Adaptive Control, Method of Averaging)","abstract":"A three-step procedure for the analysis of slowly adapting systems is presented. First, conditions are given for the existence of an integral manifold upon which the slow adaptation occurs in either continuous or discrete time. Second, conditions are derived under which this integral manifold is exponentially attractive. Third, the behavior on the manifold is analyzed via the method of averaging. In the process of developing the discrete-time part of these results, the relationship between the method of averaging for deterministic signals and the ordinary differential equation approach to the study of stochastic adaptive systems is clarified.","abstract_html":"A three-step procedure for the analysis of slowly adapting systems is presented. First, conditions are given for the existence of an integral manifold upon which the slow adaptation occurs in either continuous or discrete time. Second, conditions are derived under which this integral manifold is exponentially attractive. Third, the behavior on the manifold is analyzed via the method of averaging. In the process of developing the discrete-time part of these results, the relationship between the method of averaging for deterministic signals and the ordinary differential equation approach to the study of stochastic adaptive systems is clarified.","abstract_has_math":false,"creators":["Riedle, Bradley Dean"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-15T19:05:13Z","date_published":"2014-12-15T19:05:13Z","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)AAI8701598"],"render_values":[{"text":"(UMI)AAI8701598","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/69348","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Riedle, Bradley Dean"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-15T19:05:13Z","10000-01-01","1986"]},{"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/2142/69348","(UMI)AAI8701598"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["A three-step procedure for the analysis of slowly adapting systems is presented. First, conditions are given for the existence of an integral manifold upon which the slow adaptation occurs in either continuous or discrete time. Second, conditions are derived under which this integral manifold is exponentially attractive. Third, the behavior on the manifold is analyzed via the method of averaging. In the process of developing the discrete-time part of these results, the relationship between the method of averaging for deterministic signals and the ordinary differential equation approach to the study of stochastic adaptive systems is clarified.","This three-step procedure for analysis is then used as a design tool. First, a model reference adaptive control scheme which allows a reduced number of adjustable parameters is presented and analyzed via the three-step procedure. The scheme allows considerable flexibility in the controller parametrization. Taking advantage of this flexibility requires the use of a priori information about the plant to be controlled. Hence, the scheme provides a mechanism for using information available before the commissioning of a control system to reduce the number of adjustable controller parameters. The ideas involved in the design of this model reference adaptive control scheme are then generalized to provide guidelines for the design of slowly adapting systems. An example then illustrates the use of these guidelines to upgrade an existing fixed parameter controller to a slowly adapting one.","Made available in DSpace on 2014-12-15T19:05:13Z (GMT). No. of bitstreams: 1 8701598.pdf: 4082954 bytes, checksum: 28eadb328620b91b0c58f898dbfd7a3a (MD5) Previous issue date: 1986","Embargo set by: Seth Robbins for item 69514 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, 1986."]},{"key":"dc:title","label":"Title","values":["Integral Manifolds of Slow Adaptation (Adaptive Control, Method of Averaging)"]}]}],"canonical_facts":{"dc:creator":["Riedle, Bradley Dean"],"dc:date":["2014-12-15T19:05:13Z","10000-01-01","1986"],"dc:description":["A three-step procedure for the analysis of slowly adapting systems is presented. First, conditions are given for the existence of an integral manifold upon which the slow adaptation occurs in either continuous or discrete time. Second, conditions are derived under which this integral manifold is exponentially attractive. Third, the behavior on the manifold is analyzed via the method of averaging. In the process of developing the discrete-time part of these results, the relationship between the method of averaging for deterministic signals and the ordinary differential equation approach to the study of stochastic adaptive systems is clarified.","This three-step procedure for analysis is then used as a design tool. First, a model reference adaptive control scheme which allows a reduced number of adjustable parameters is presented and analyzed via the three-step procedure. The scheme allows considerable flexibility in the controller parametrization. Taking advantage of this flexibility requires the use of a priori information about the plant to be controlled. Hence, the scheme provides a mechanism for using information available before the commissioning of a control system to reduce the number of adjustable controller parameters. The ideas involved in the design of this model reference adaptive control scheme are then generalized to provide guidelines for the design of slowly adapting systems. An example then illustrates the use of these guidelines to upgrade an existing fixed parameter controller to a slowly adapting one.","Made available in DSpace on 2014-12-15T19:05:13Z (GMT). No. of bitstreams: 1 8701598.pdf: 4082954 bytes, checksum: 28eadb328620b91b0c58f898dbfd7a3a (MD5) Previous issue date: 1986","Embargo set by: Seth Robbins for item 69514 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, 1986."],"dc:identifier":["http://hdl.handle.net/2142/69348","(UMI)AAI8701598"],"dc:subject":["Engineering, Electronics and Electrical"],"dc:title":["Integral Manifolds of Slow Adaptation (Adaptive Control, Method of Averaging)"],"dc:type":["text"],"thesis:degree_discipline":["Electrical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:00Z"}