{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/80825"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/80825","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Robust Control of Stochastic Nonlinear Systems","abstract":"The third topic studied involves the constrained minimax optimization problem for a class of stochastic nonlinear systems in strict-feedback form, where in addition to the standard Wiener process there is a norm-bounded unknown disturbance driving the system. The bound on the disturbance is a stochastic integral quadratic constraint, and it is also related to the constraint on the relative entropy between the uncertainty probability measure and the reference probability measure on the original probability space. Within this structure, by first converting the original constrained optimization problem into an unconstrained one (a stochastic differential game) and then making use of the duality relationship between stochastic games and risk-sensitive stochastic control, we obtain a minimax state-feedback control law that is both locally optimal and globally inverse optimal. Furthermore, the closed-loop system is absolutely stable in the presence of stochastic uncertainty disturbances.","abstract_html":"The third topic studied involves the constrained minimax optimization problem for a class of stochastic nonlinear systems in strict-feedback form, where in addition to the standard Wiener process there is a norm-bounded unknown disturbance driving the system. The bound on the disturbance is a stochastic integral quadratic constraint, and it is also related to the constraint on the relative entropy between the uncertainty probability measure and the reference probability measure on the original probability space. Within this structure, by first converting the original constrained optimization problem into an unconstrained one (a stochastic differential game) and then making use of the duality relationship between stochastic games and risk-sensitive stochastic control, we obtain a minimax state-feedback control law that is both locally optimal and globally inverse optimal. Furthermore, the closed-loop system is absolutely stable in the presence of stochastic uncertainty disturbances.","abstract_has_math":false,"creators":["Tang, Cheng"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical Engineering","degree_department":null,"school":null,"contributors":["Basar, Tamer"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:08:21Z","date_published":"2015-09-25T20:08:21Z","updated_at":"2026-07-22T22:26:15Z","subjects":["Engineering, Electronics and Electrical"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3086197"],"render_values":[{"text":"(MiAaPQ)AAI3086197","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/80825","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Basar, Tamer"]},{"key":"dc:creator","label":"Author","values":["Tang, Cheng"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:08:21Z","10000-01-01","2003"]},{"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":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/80825","(MiAaPQ)AAI3086197"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["The third topic studied involves the constrained minimax optimization problem for a class of stochastic nonlinear systems in strict-feedback form, where in addition to the standard Wiener process there is a norm-bounded unknown disturbance driving the system. The bound on the disturbance is a stochastic integral quadratic constraint, and it is also related to the constraint on the relative entropy between the uncertainty probability measure and the reference probability measure on the original probability space. Within this structure, by first converting the original constrained optimization problem into an unconstrained one (a stochastic differential game) and then making use of the duality relationship between stochastic games and risk-sensitive stochastic control, we obtain a minimax state-feedback control law that is both locally optimal and globally inverse optimal. Furthermore, the closed-loop system is absolutely stable in the presence of stochastic uncertainty disturbances.","Made available in DSpace on 2015-09-25T20:08:21Z (GMT). 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The bound on the disturbance is a stochastic integral quadratic constraint, and it is also related to the constraint on the relative entropy between the uncertainty probability measure and the reference probability measure on the original probability space. Within this structure, by first converting the original constrained optimization problem into an unconstrained one (a stochastic differential game) and then making use of the duality relationship between stochastic games and risk-sensitive stochastic control, we obtain a minimax state-feedback control law that is both locally optimal and globally inverse optimal. Furthermore, the closed-loop system is absolutely stable in the presence of stochastic uncertainty disturbances.","Made available in DSpace on 2015-09-25T20:08:21Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3086197.pdf: 4642020 bytes, checksum: fe8abdad0ab4ffc4d69d0d4cc121a68e (MD5) Previous issue date: 2003","Embargo set by: Seth Robbins for item 82107 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","106 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2003."],"dc:identifier":["http://hdl.handle.net/2142/80825","(MiAaPQ)AAI3086197"],"dc:language":["eng"],"dc:subject":["Engineering, Electronics and Electrical"],"dc:title":["Robust Control of Stochastic Nonlinear Systems"],"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":"2026-07-22T22:26:15Z"}