{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/82478"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/82478","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"A General Framework for the Control of Nonlinear Systems","abstract":"One of the main roadblocks in developing effective controller design techniques for nonlinear processes is the lack of a nonconservative framework for analyzing the closed loop stability and performance of generic nonlinear dynamical systems. Such a framework can be developed for systems consisting of interconnections of linear systems and bounded nonlinear operators. The use of the Standard Nonlinear Operator Form (SNOF) is proposed for the control of nonlinear systems. The SNOF is a linear system with a static diagonal nonlinear operator in feedback. It is shown that nonlinear systems written as SNOF's can approximate any nonlinear dynamical system to any degree of precision. This thesis focuses on a nonlinear stability analysis and performance framework designed around Dynamic Artificial Neural network (DANN) systems to produce computationally-feasible tools to analyze the stability and performance of these systems. The nonlinear stability analysis tools are formulated for discrete-time systems as feasibility problems over Linear Matrix Inequality (LMI) constraints. A Lur'e-Lyapunov function is used, and general properties of the nonlinear elements are exploited to reduce conservatism. The stability analysis conditions are extended to allow the quantification of the performance, measured in terms of a worst-case induced 2-norm. It is also described how the performance analysis condition can be used within an optimization-based formulation to design nonlinear optimal-feedback controllers.","abstract_html":"One of the main roadblocks in developing effective controller design techniques for nonlinear processes is the lack of a nonconservative framework for analyzing the closed loop stability and performance of generic nonlinear dynamical systems. Such a framework can be developed for systems consisting of interconnections of linear systems and bounded nonlinear operators. The use of the Standard Nonlinear Operator Form (SNOF) is proposed for the control of nonlinear systems. The SNOF is a linear system with a static diagonal nonlinear operator in feedback. It is shown that nonlinear systems written as SNOF's can approximate any nonlinear dynamical system to any degree of precision. This thesis focuses on a nonlinear stability analysis and performance framework designed around Dynamic Artificial Neural network (DANN) systems to produce computationally-feasible tools to analyze the stability and performance of these systems. The nonlinear stability analysis tools are formulated for discrete-time systems as feasibility problems over Linear Matrix Inequality (LMI) constraints. A Lur'e-Lyapunov function is used, and general properties of the nonlinear elements are exploited to reduce conservatism. The stability analysis conditions are extended to allow the quantification of the performance, measured in terms of a worst-case induced 2-norm. It is also described how the performance analysis condition can be used within an optimization-based formulation to design nonlinear optimal-feedback controllers.","abstract_has_math":false,"creators":["Rios-Patron, Ernesto"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemical Engineering","degree_department":null,"school":null,"contributors":["Braatz, Richard D."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-25T20:44:17Z","date_published":"2015-09-25T20:44:17Z","updated_at":"2026-07-22T22:26:18Z","subjects":["Engineering, Chemical"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI9971176"],"render_values":[{"text":"(MiAaPQ)AAI9971176","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/82478","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Braatz, Richard D."]},{"key":"dc:creator","label":"Author","values":["Rios-Patron, Ernesto"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-25T20:44:17Z","10000-01-01","2000"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemical 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, Chemical"]}]},{"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/2142/82478","(MiAaPQ)AAI9971176"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["One of the main roadblocks in developing effective controller design techniques for nonlinear processes is the lack of a nonconservative framework for analyzing the closed loop stability and performance of generic nonlinear dynamical systems. 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