{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22885"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22885","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Sensitivity methods and slow adaptation","abstract":"In many existing model reference adaptive control (MRAC) schemes, the plant order and relative degree are assumed known. Then a full-order control parameterization is specified which allows for an exact transfer function match between the closed-loop plant and a reference model. Often for plants of modest complexity, this leads to a large number of adjustable parameters. Apart from the computational burden, an excessive parameterization imposes, a common assumption used to prove global stability requires the regressor to be Persistently Exciting (PE). This PE requirement has been tied to the spectral content of the system input, and is directly proportional to the number of parameters adjusted. Often this imposes unrealizable requirements upon the system input. This problem is especially pronounced for regulation problems where the reference and system input are zero.","abstract_html":"In many existing model reference adaptive control (MRAC) schemes, the plant order and relative degree are assumed known. Then a full-order control parameterization is specified which allows for an exact transfer function match between the closed-loop plant and a reference model. Often for plants of modest complexity, this leads to a large number of adjustable parameters. Apart from the computational burden, an excessive parameterization imposes, a common assumption used to prove global stability requires the regressor to be Persistently Exciting (PE). This PE requirement has been tied to the spectral content of the system input, and is directly proportional to the number of parameters adjusted. Often this imposes unrealizable requirements upon the system input. This problem is especially pronounced for regulation problems where the reference and system input are zero.","abstract_has_math":false,"creators":["Rhode, Douglas Scott"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical and Computer Engineering","degree_department":null,"school":null,"contributors":["Kokotovic, P.V."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:54:45Z","date_published":"2011-05-07T13:54:45Z","updated_at":"2026-07-22T22:25:20Z","subjects":["Engineering, System Science"],"languages":["eng"],"rights":["Copyright 1990 Rhode, Douglas Scott"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9026301","(UMI)AAI9026301"],"render_values":[{"text":"AAI9026301","href":null,"code":true},{"text":"(UMI)AAI9026301","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22885","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kokotovic, P.V."]},{"key":"dc:creator","label":"Author","values":["Rhode, Douglas Scott"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:54:45Z","10000-01-01","1990"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical and Computer 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, System Science"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1990 Rhode, Douglas Scott"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9026301","(UMI)AAI9026301","http://hdl.handle.net/2142/22885"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In many existing model reference adaptive control (MRAC) schemes, the plant order and relative degree are assumed known. Then a full-order control parameterization is specified which allows for an exact transfer function match between the closed-loop plant and a reference model. Often for plants of modest complexity, this leads to a large number of adjustable parameters. Apart from the computational burden, an excessive parameterization imposes, a common assumption used to prove global stability requires the regressor to be Persistently Exciting (PE). This PE requirement has been tied to the spectral content of the system input, and is directly proportional to the number of parameters adjusted. Often this imposes unrealizable requirements upon the system input. This problem is especially pronounced for regulation problems where the reference and system input are zero.","In the approach presented in this thesis, the number of parameters and structure of the controller will not be tied to plant order. Instead, a reduced-order parameterization such as PID or lead-lag will be adapted. For many applications, slow adaptation offers an attractive means of increasing performance while retaining the simplicity of the underlying linear system.","Recent developments in integral manifolds and averaging are combined with sensitivity results from the 1960s to construct a pseudogradient approach to slow adaptation. Under slow adaptation, the parameters change much slower than the state of the underlying linear system. An integral manifold, the slow manifold, is used to separate the slow parameter dynamics from the fast linear states. This slow manifold can be approximated by a frozen parameter manifold, which is simply the steady-state response of the linear system with the parameters held constant. The signals from the frozen manifold are then substituted into the parameter update equation. This equation is then averaged to produce a set of nonlinear time invariant equations which approximate the dynamics of the parameters. Using sensitivity techniques, a pseudogradient algorithm will be constructed such that the averaged system will approximate a steepest descent optimization algorithm to reduce the mean square output error. This approach will encompass several existing algorithms such as those proposed by Narendra and Bodson (1,2). Sufficient conditions are given to guarantee the stability of these pseudogradient algorithms.","Made available in DSpace on 2011-05-07T13:54:45Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9026301.pdf: 2454341 bytes, checksum: ee7ff90857f72330c61efec97520938e (MD5) Previous issue date: 1990","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:00:41Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:28:44-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Sensitivity methods and slow adaptation"]}]}],"canonical_facts":{"dc:contributor":["Kokotovic, P.V."],"dc:creator":["Rhode, Douglas Scott"],"dc:date":["2011-05-07T13:54:45Z","10000-01-01","1990"],"dc:description":["In many existing model reference adaptive control (MRAC) schemes, the plant order and relative degree are assumed known. Then a full-order control parameterization is specified which allows for an exact transfer function match between the closed-loop plant and a reference model. Often for plants of modest complexity, this leads to a large number of adjustable parameters. Apart from the computational burden, an excessive parameterization imposes, a common assumption used to prove global stability requires the regressor to be Persistently Exciting (PE). This PE requirement has been tied to the spectral content of the system input, and is directly proportional to the number of parameters adjusted. Often this imposes unrealizable requirements upon the system input. This problem is especially pronounced for regulation problems where the reference and system input are zero.","In the approach presented in this thesis, the number of parameters and structure of the controller will not be tied to plant order. Instead, a reduced-order parameterization such as PID or lead-lag will be adapted. For many applications, slow adaptation offers an attractive means of increasing performance while retaining the simplicity of the underlying linear system.","Recent developments in integral manifolds and averaging are combined with sensitivity results from the 1960s to construct a pseudogradient approach to slow adaptation. Under slow adaptation, the parameters change much slower than the state of the underlying linear system. An integral manifold, the slow manifold, is used to separate the slow parameter dynamics from the fast linear states. This slow manifold can be approximated by a frozen parameter manifold, which is simply the steady-state response of the linear system with the parameters held constant. The signals from the frozen manifold are then substituted into the parameter update equation. This equation is then averaged to produce a set of nonlinear time invariant equations which approximate the dynamics of the parameters. Using sensitivity techniques, a pseudogradient algorithm will be constructed such that the averaged system will approximate a steepest descent optimization algorithm to reduce the mean square output error. This approach will encompass several existing algorithms such as those proposed by Narendra and Bodson (1,2). Sufficient conditions are given to guarantee the stability of these pseudogradient algorithms.","Made available in DSpace on 2011-05-07T13:54:45Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9026301.pdf: 2454341 bytes, checksum: ee7ff90857f72330c61efec97520938e (MD5) Previous issue date: 1990","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T15:00:41Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:28:44-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"],"dc:identifier":["AAI9026301","(UMI)AAI9026301","http://hdl.handle.net/2142/22885"],"dc:language":["eng"],"dc:rights":["Copyright 1990 Rhode, Douglas Scott"],"dc:subject":["Engineering, System Science"],"dc:title":["Sensitivity methods and slow adaptation"],"dc:type":["text"],"thesis:degree_discipline":["Electrical and Computer Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:20Z"}