{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/102412"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/102412","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Receding-horizon switched linear system design: a semidefinite programming approach with distributed computation","abstract":"This dissertation presents a framework for analysis and controller synthesis problems for switched linear systems. These are multi-modal systems whose parameters vary within a finite set according to the state of a discrete time automaton; the switching signal may be unconstrained or may be drawn from a language of admissible switching signals. This model of system dynamics and discrete logic has many applications in a number of engineering contexts. A receding-horizon type approach is taken by designing controllers with access to a finite-length preview of future modes and finite memory of past modes; the length of both preview and memory are taken as design choices. The results developed here take the form of nested sequences of SDP feasibility problems. These conditions are exact in that the feasibility of any element of the sequence is sufficient to construct a suitable controller, while the existence of a suitable controller necessitates the feasibility of some element of the sequence. Considered first is the problem of controller synthesis for the stabilization of switched systems. These developments serve both as a control problem of interest and a demonstration of the methods used to solve subsequent switched control problems. Exact conditions for the existence of a controller are developed, along with converse results which rule out levels of closed-loop stability based on the infeasibility of individual SDP problems. This permits the achievable closed-loop performance level to be approximated to arbitrary accuracy. Examined next are two different performance problems: one of disturbance attenuation and one of windowed variance. For each problem, controller synthesis conditions are presented exactly in the form of SDP feasibility problems which may be optimized to determine levels of performance. In both cases, the performance level may be taken as uniform or allowed to vary based on the switching path encountered. The controller synthesis conditions presented here can grow both large and computationally intensive, but they share a common structural sparsity which may be exploited. The last part of this dissertation examines this structure and presents a distributed approach to solving such problems. This maintains the tractability of these results even at large scales, expanding the scope of systems to which these methods can be applied.","abstract_html":"This dissertation presents a framework for analysis and controller synthesis problems for switched linear systems. These are multi-modal systems whose parameters vary within a finite set according to the state of a discrete time automaton; the switching signal may be unconstrained or may be drawn from a language of admissible switching signals. This model of system dynamics and discrete logic has many applications in a number of engineering contexts. A receding-horizon type approach is taken by designing controllers with access to a finite-length preview of future modes and finite memory of past modes; the length of both preview and memory are taken as design choices. The results developed here take the form of nested sequences of SDP feasibility problems. These conditions are exact in that the feasibility of any element of the sequence is sufficient to construct a suitable controller, while the existence of a suitable controller necessitates the feasibility of some element of the sequence. Considered first is the problem of controller synthesis for the stabilization of switched systems. These developments serve both as a control problem of interest and a demonstration of the methods used to solve subsequent switched control problems. Exact conditions for the existence of a controller are developed, along with converse results which rule out levels of closed-loop stability based on the infeasibility of individual SDP problems. This permits the achievable closed-loop performance level to be approximated to arbitrary accuracy. Examined next are two different performance problems: one of disturbance attenuation and one of windowed variance. For each problem, controller synthesis conditions are presented exactly in the form of SDP feasibility problems which may be optimized to determine levels of performance. In both cases, the performance level may be taken as uniform or allowed to vary based on the switching path encountered. The controller synthesis conditions presented here can grow both large and computationally intensive, but they share a common structural sparsity which may be exploited. The last part of this dissertation examines this structure and presents a distributed approach to solving such problems. This maintains the tractability of these results even at large scales, expanding the scope of systems to which these methods can be applied.","abstract_has_math":false,"creators":["Essick V, Raymond B."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Dullerud, Geir E.","Liberzon, Daniel M.","Salapaka, Srinivasa M.","Voulgaris, Petros G.","Jungers, Raphael M."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-02-06T19:32:44Z","date_published":"2019-02-06T19:32:44Z","updated_at":"2026-07-22T22:24:40Z","subjects":["Switched linear systems","convex control","distributed semidefinite programming"],"languages":["en"],"rights":["Copyright 2018 Raymond B Essick V"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/102412","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dullerud, Geir E.","Liberzon, Daniel M.","Salapaka, Srinivasa M.","Voulgaris, Petros G.","Jungers, Raphael M."]},{"key":"dc:creator","label":"Author","values":["Essick V, Raymond B."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019-02-06T19:32:44Z","2018-10-22","2018-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical 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":["Switched linear systems","convex control","distributed semidefinite programming"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Raymond B Essick V"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/102412"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This dissertation presents a framework for analysis and controller synthesis problems for switched linear systems. These are multi-modal systems whose parameters vary within a finite set according to the state of a discrete time automaton; the switching signal may be unconstrained or may be drawn from a language of admissible switching signals. This model of system dynamics and discrete logic has many applications in a number of engineering contexts. A receding-horizon type approach is taken by designing controllers with access to a finite-length preview of future modes and finite memory of past modes; the length of both preview and memory are taken as design choices. The results developed here take the form of nested sequences of SDP feasibility problems. These conditions are exact in that the feasibility of any element of the sequence is sufficient to construct a suitable controller, while the existence of a suitable controller necessitates the feasibility of some element of the sequence. Considered first is the problem of controller synthesis for the stabilization of switched systems. These developments serve both as a control problem of interest and a demonstration of the methods used to solve subsequent switched control problems. Exact conditions for the existence of a controller are developed, along with converse results which rule out levels of closed-loop stability based on the infeasibility of individual SDP problems. This permits the achievable closed-loop performance level to be approximated to arbitrary accuracy. Examined next are two different performance problems: one of disturbance attenuation and one of windowed variance. For each problem, controller synthesis conditions are presented exactly in the form of SDP feasibility problems which may be optimized to determine levels of performance. In both cases, the performance level may be taken as uniform or allowed to vary based on the switching path encountered. The controller synthesis conditions presented here can grow both large and computationally intensive, but they share a common structural sparsity which may be exploited. The last part of this dissertation examines this structure and presents a distributed approach to solving such problems. This maintains the tractability of these results even at large scales, expanding the scope of systems to which these methods can be applied.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-02-05 without embargo terms","The student, Raymond Essick V, accepted the attached license on 2018-10-16 at 21:27.","The student, Raymond Essick V, submitted this Dissertation for approval on 2018-10-16 at 21:37.","This Dissertation was approved for publication on 2018-10-22 at 15:08.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13035 on 2019-02-05 at 11:08:24","Made available in DSpace on 2019-02-06T19:32:44Z (GMT). No. of bitstreams: 4 ESSICKV-DISSERTATION-2018.pdf: 473221 bytes, checksum: 23245eb30e64b2e5a92cd38722d1bb5e (MD5) phd_dissertation.zip: 2129464 bytes, checksum: 8fcb47d31024d8b5e1428d96b36a08a4 (MD5) LICENSE.txt: 4211 bytes, checksum: dac8856984772f8ba364a5e8b882c4fe (MD5) PROQUEST_LICENSE.txt: 4557 bytes, checksum: 4cfc400b78117041fc5abc5708c3aa9c (MD5) Previous issue date: 2018-10-22"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Receding-horizon switched linear system design: a semidefinite programming approach with distributed computation"]}]}],"canonical_facts":{"dc:contributor":["Dullerud, Geir E.","Liberzon, Daniel M.","Salapaka, Srinivasa M.","Voulgaris, Petros G.","Jungers, Raphael M."],"dc:creator":["Essick V, Raymond B."],"dc:date":["2019-02-06T19:32:44Z","2018-10-22","2018-12"],"dc:description":["This dissertation presents a framework for analysis and controller synthesis problems for switched linear systems. These are multi-modal systems whose parameters vary within a finite set according to the state of a discrete time automaton; the switching signal may be unconstrained or may be drawn from a language of admissible switching signals. This model of system dynamics and discrete logic has many applications in a number of engineering contexts. A receding-horizon type approach is taken by designing controllers with access to a finite-length preview of future modes and finite memory of past modes; the length of both preview and memory are taken as design choices. The results developed here take the form of nested sequences of SDP feasibility problems. These conditions are exact in that the feasibility of any element of the sequence is sufficient to construct a suitable controller, while the existence of a suitable controller necessitates the feasibility of some element of the sequence. Considered first is the problem of controller synthesis for the stabilization of switched systems. These developments serve both as a control problem of interest and a demonstration of the methods used to solve subsequent switched control problems. Exact conditions for the existence of a controller are developed, along with converse results which rule out levels of closed-loop stability based on the infeasibility of individual SDP problems. This permits the achievable closed-loop performance level to be approximated to arbitrary accuracy. Examined next are two different performance problems: one of disturbance attenuation and one of windowed variance. For each problem, controller synthesis conditions are presented exactly in the form of SDP feasibility problems which may be optimized to determine levels of performance. In both cases, the performance level may be taken as uniform or allowed to vary based on the switching path encountered. The controller synthesis conditions presented here can grow both large and computationally intensive, but they share a common structural sparsity which may be exploited. The last part of this dissertation examines this structure and presents a distributed approach to solving such problems. This maintains the tractability of these results even at large scales, expanding the scope of systems to which these methods can be applied.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-02-05 without embargo terms","The student, Raymond Essick V, accepted the attached license on 2018-10-16 at 21:27.","The student, Raymond Essick V, submitted this Dissertation for approval on 2018-10-16 at 21:37.","This Dissertation was approved for publication on 2018-10-22 at 15:08.","DSpace SAF Submission Ingestion Package generated from Vireo submission #13035 on 2019-02-05 at 11:08:24","Made available in DSpace on 2019-02-06T19:32:44Z (GMT). No. of bitstreams: 4 ESSICKV-DISSERTATION-2018.pdf: 473221 bytes, checksum: 23245eb30e64b2e5a92cd38722d1bb5e (MD5) phd_dissertation.zip: 2129464 bytes, checksum: 8fcb47d31024d8b5e1428d96b36a08a4 (MD5) LICENSE.txt: 4211 bytes, checksum: dac8856984772f8ba364a5e8b882c4fe (MD5) PROQUEST_LICENSE.txt: 4557 bytes, checksum: 4cfc400b78117041fc5abc5708c3aa9c (MD5) Previous issue date: 2018-10-22"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/102412"],"dc:language":["en"],"dc:rights":["Copyright 2018 Raymond B Essick V"],"dc:subject":["Switched linear systems","convex control","distributed semidefinite programming"],"dc:title":["Receding-horizon switched linear system design: a semidefinite programming approach with distributed computation"],"dc:type":["text"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:40Z"}