{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/106210"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/106210","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Morphisms of networks of hybrid open systems","abstract":"This dissertation develops a theory of networks of hybrid open systems and morphisms. This theory builds upon a framework of networks of continuous-time open systems as product and interconnection. We work out categorical notions for hybrid systems, deterministic hybrid systems, hybrid open systems, networks of hybrid open systems, and morphisms of networks of hybrid open systems. We also develop categorical notions for abstract systems, abstract open systems, networks of abstract open systems, and morphisms of networks of abstract open systems. We show that a collection of relations holding among pairs of systems induces a relation between interconnected systems. We use this result for abstract systems to prove a corresponding result for networks of hybrid systems. This result translates as saying that our procedure for building networks preserves morphisms of open systems: a collection of morphisms of (sub)systems is sent to a morphism of networked systems. We thus both justify our formalism and concretize the intuition that a network is a collection of systems pieced together in a certain way.","abstract_html":"This dissertation develops a theory of networks of hybrid open systems and morphisms. This theory builds upon a framework of networks of continuous-time open systems as product and interconnection. We work out categorical notions for hybrid systems, deterministic hybrid systems, hybrid open systems, networks of hybrid open systems, and morphisms of networks of hybrid open systems. We also develop categorical notions for abstract systems, abstract open systems, networks of abstract open systems, and morphisms of networks of abstract open systems. We show that a collection of relations holding among pairs of systems induces a relation between interconnected systems. We use this result for abstract systems to prove a corresponding result for networks of hybrid systems. This result translates as saying that our procedure for building networks preserves morphisms of open systems: a collection of morphisms of (sub)systems is sent to a morphism of networked systems. We thus both justify our formalism and concretize the intuition that a network is a collection of systems pieced together in a certain way.","abstract_has_math":false,"creators":["Schmidt, Arnold James"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Lerman, Eugene","DeVille, Lee","Berwick-Evans, Dan","Nijholt, Eddie"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2020,"date_issued":"2020-03-02T21:58:15Z","date_published":"2020-03-02T21:58:15Z","updated_at":"2026-07-22T22:24:45Z","subjects":["networks of open systems, hybrid systems, category theory, control systems, dynamical systems"],"languages":["en"],"rights":["Copyright 2019 by Arnold James Schmidt. All rights reserved."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/106210","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Lerman, Eugene","DeVille, Lee","Berwick-Evans, Dan","Nijholt, Eddie"]},{"key":"dc:creator","label":"Author","values":["Schmidt, Arnold James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2020-03-02T21:58:15Z","2019-12-06","2019-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"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":["networks of open systems, hybrid systems, category theory, control systems, dynamical systems"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2019 by Arnold James Schmidt. 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We use this result for abstract systems to prove a corresponding result for networks of hybrid systems. This result translates as saying that our procedure for building networks preserves morphisms of open systems: a collection of morphisms of (sub)systems is sent to a morphism of networked systems. We thus both justify our formalism and concretize the intuition that a network is a collection of systems pieced together in a certain way.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-02-28 without embargo terms","The student, Arnold Schmidt, accepted the attached license on 2019-11-24 at 15:12.","The student, Arnold Schmidt, submitted this Dissertation for approval on 2019-11-24 at 21:22.","This Dissertation was approved for publication on 2019-12-06 at 07:36.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14602 on 2020-02-28 at 17:14:10","Made available in DSpace on 2020-03-02T21:58:15Z (GMT). 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We work out categorical notions for hybrid systems, deterministic hybrid systems, hybrid open systems, networks of hybrid open systems, and morphisms of networks of hybrid open systems. We also develop categorical notions for abstract systems, abstract open systems, networks of abstract open systems, and morphisms of networks of abstract open systems. We show that a collection of relations holding among pairs of systems induces a relation between interconnected systems. We use this result for abstract systems to prove a corresponding result for networks of hybrid systems. This result translates as saying that our procedure for building networks preserves morphisms of open systems: a collection of morphisms of (sub)systems is sent to a morphism of networked systems. We thus both justify our formalism and concretize the intuition that a network is a collection of systems pieced together in a certain way.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2020-02-28 without embargo terms","The student, Arnold Schmidt, accepted the attached license on 2019-11-24 at 15:12.","The student, Arnold Schmidt, submitted this Dissertation for approval on 2019-11-24 at 21:22.","This Dissertation was approved for publication on 2019-12-06 at 07:36.","DSpace SAF Submission Ingestion Package generated from Vireo submission #14602 on 2020-02-28 at 17:14:10","Made available in DSpace on 2020-03-02T21:58:15Z (GMT). No. of bitstreams: 3 SCHMIDT-DISSERTATION-2019.pdf: 857674 bytes, checksum: 3ec3a155e6cde8cbab79fd8276d9b647 (MD5) LICENSE.txt: 4210 bytes, checksum: eb2f65fdbfa8b0a7bba4b32cc0c5a16b (MD5) PROQUEST_LICENSE.txt: 4556 bytes, checksum: 05b5553a08c98ff184172309813a066c (MD5) Previous issue date: 2019-12-06"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/106210"],"dc:language":["en"],"dc:rights":["Copyright 2019 by Arnold James Schmidt. All rights reserved."],"dc:subject":["networks of open systems, hybrid systems, category theory, control systems, dynamical systems"],"dc:title":["Morphisms of networks of hybrid open systems"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:45Z"}