{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/107850"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/107850","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Nonlinear and switched systems: Geometric motion planning, non-monotonic Lyapunov functions and input-to-state stability","abstract":"\"Both synthesis of control strategy for motion planning and analysis of stability of nonlinear and switched systems have been researched in this work. In terms of control strategy, we propose a novel approach to the long-standing problem of motion planning for non-holonomic systems. The admissible motion is obtained by properly assigning \"\"length\"\" to the motion trajectories which penalizes them in the inadmissible directions, and \"\"deforming\"\" them in order to minimize the \"\"length\"\" via solving a set of parabolic partial differential equations. Several variations of the fundamental motion planning problem are also considered in this work. In terms of stability analysis, we have studied two approaches related to non-monotonic Lyapunov functions. More explicitly, the techniques of \"\"almost Lyapunov\"\" functions and higher order derivatives of Lyapunov functions -- which were used to study the stability of autonomous nonlinear systems in the literature -- are generalized to nonlinear systems with inputs. Under some mild assumptions, the nonlinear systems can be proven to be input-to-state stable using these techniques of non-monotonic Lyapunov functions. In addition, the methodology used in the derivation can also be used to show the equivalence between several stability properties of state-dependent switched systems.\"","abstract_html":""Both synthesis of control strategy for motion planning and analysis of stability of nonlinear and switched systems have been researched in this work. In terms of control strategy, we propose a novel approach to the long-standing problem of motion planning for non-holonomic systems. The admissible motion is obtained by properly assigning ""length"" to the motion trajectories which penalizes them in the inadmissible directions, and ""deforming"" them in order to minimize the ""length"" via solving a set of parabolic partial differential equations. Several variations of the fundamental motion planning problem are also considered in this work. In terms of stability analysis, we have studied two approaches related to non-monotonic Lyapunov functions. More explicitly, the techniques of ""almost Lyapunov"" functions and higher order derivatives of Lyapunov functions -- which were used to study the stability of autonomous nonlinear systems in the literature -- are generalized to nonlinear systems with inputs. Under some mild assumptions, the nonlinear systems can be proven to be input-to-state stable using these techniques of non-monotonic Lyapunov functions. In addition, the methodology used in the derivation can also be used to show the equivalence between several stability properties of state-dependent switched systems."","abstract_has_math":false,"creators":["Liu, Shenyu"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Liberzon, Daniel","Belabbas, Mohamed-Ali","Zharnitsky, Vadim","Baryshnikov, Yuliy"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-08-26T21:53:56Z","date_published":"2020-08-26T21:53:56Z","updated_at":"2026-07-22T22:24:47Z","subjects":["Nonlinear systems","switched systems","motion planning","Lyapunov approach","input-to-state stability"],"languages":["en"],"rights":["Copyright 2020 Shenyu Liu"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/107850","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Liberzon, Daniel","Belabbas, Mohamed-Ali","Zharnitsky, Vadim","Baryshnikov, Yuliy"]},{"key":"dc:creator","label":"Author","values":["Liu, Shenyu"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-08-26T21:53:56Z","2020-01-31","2020-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"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":["Nonlinear systems","switched systems","motion planning","Lyapunov approach","input-to-state stability"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2020 Shenyu Liu"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/107850"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"Both synthesis of control strategy for motion planning and analysis of stability of nonlinear and switched systems have been researched in this work. In terms of control strategy, we propose a novel approach to the long-standing problem of motion planning for non-holonomic systems. The admissible motion is obtained by properly assigning \"\"length\"\" to the motion trajectories which penalizes them in the inadmissible directions, and \"\"deforming\"\" them in order to minimize the \"\"length\"\" via solving a set of parabolic partial differential equations. Several variations of the fundamental motion planning problem are also considered in this work. In terms of stability analysis, we have studied two approaches related to non-monotonic Lyapunov functions. More explicitly, the techniques of \"\"almost Lyapunov\"\" functions and higher order derivatives of Lyapunov functions -- which were used to study the stability of autonomous nonlinear systems in the literature -- are generalized to nonlinear systems with inputs. Under some mild assumptions, the nonlinear systems can be proven to be input-to-state stable using these techniques of non-monotonic Lyapunov functions. In addition, the methodology used in the derivation can also be used to show the equivalence between several stability properties of state-dependent switched systems.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-08-25 without embargo terms","The student, Shenyu Liu, accepted the attached license on 2020-01-30 at 15:48.","The student, Shenyu Liu, submitted this Dissertation for approval on 2020-01-30 at 16:07.","This Dissertation was approved for publication on 2020-01-31 at 09:21.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14863 on 2020-08-25 at 17:03:22","Made available in DSpace on 2020-08-26T21:53:56Z (GMT). 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In terms of control strategy, we propose a novel approach to the long-standing problem of motion planning for non-holonomic systems. The admissible motion is obtained by properly assigning \"\"length\"\" to the motion trajectories which penalizes them in the inadmissible directions, and \"\"deforming\"\" them in order to minimize the \"\"length\"\" via solving a set of parabolic partial differential equations. Several variations of the fundamental motion planning problem are also considered in this work. In terms of stability analysis, we have studied two approaches related to non-monotonic Lyapunov functions. More explicitly, the techniques of \"\"almost Lyapunov\"\" functions and higher order derivatives of Lyapunov functions -- which were used to study the stability of autonomous nonlinear systems in the literature -- are generalized to nonlinear systems with inputs. Under some mild assumptions, the nonlinear systems can be proven to be input-to-state stable using these techniques of non-monotonic Lyapunov functions. In addition, the methodology used in the derivation can also be used to show the equivalence between several stability properties of state-dependent switched systems.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-08-25 without embargo terms","The student, Shenyu Liu, accepted the attached license on 2020-01-30 at 15:48.","The student, Shenyu Liu, submitted this Dissertation for approval on 2020-01-30 at 16:07.","This Dissertation was approved for publication on 2020-01-31 at 09:21.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14863 on 2020-08-25 at 17:03:22","Made available in DSpace on 2020-08-26T21:53:56Z (GMT). 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