{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/99265"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/99265","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"State estimation of switched nonlinear systems and systems with bounded inputs: Entropy and bit rates","abstract":"State estimation is a fundamental problem when monitoring and controlling dynamical systems. Engineering systems interconnect sensing and computing devices over shared bandwidth-limited channels, and therefore, estimation algorithms should strive to use bandwidth optimally. Often, the dynamics of these systems are affected by external factors. In certain cases, these factors would lead the system to switch between different modes. In other cases, they would affect the dynamics of the system continuously in time without leading to explicit mode transitions. In this thesis, we present two notions of entropy for state estimation of nonlinear switched and non-autonomous dynamical systems as lower bounds on the average number of bits needed to be sent from the sensors to the estimators to estimate the states with deterministic (worst case) error bounds. Our approach relies on the notion of topological entropy and uses techniques from control under limited information. Since the computation of these entropies is hard in general, we compute corresponding upper bounds. Additionally, we design a state estimation algorithm for switched systems when their modes cannot be observed. We show that the average bit rate used by the algorithm is optimal in the sense that the efficiency gap is within an additive constant from the gap between the entropy of the considered system and its computed upper-bound. Finally, we apply our theory and algorithms to linear and nonlinear models of systems such as a glycemic index for diabetic patients, a controller of a Harrier jet and a Pendulum.","abstract_html":"State estimation is a fundamental problem when monitoring and controlling dynamical systems. Engineering systems interconnect sensing and computing devices over shared bandwidth-limited channels, and therefore, estimation algorithms should strive to use bandwidth optimally. Often, the dynamics of these systems are affected by external factors. In certain cases, these factors would lead the system to switch between different modes. In other cases, they would affect the dynamics of the system continuously in time without leading to explicit mode transitions. In this thesis, we present two notions of entropy for state estimation of nonlinear switched and non-autonomous dynamical systems as lower bounds on the average number of bits needed to be sent from the sensors to the estimators to estimate the states with deterministic (worst case) error bounds. Our approach relies on the notion of topological entropy and uses techniques from control under limited information. Since the computation of these entropies is hard in general, we compute corresponding upper bounds. Additionally, we design a state estimation algorithm for switched systems when their modes cannot be observed. We show that the average bit rate used by the algorithm is optimal in the sense that the efficiency gap is within an additive constant from the gap between the entropy of the considered system and its computed upper-bound. Finally, we apply our theory and algorithms to linear and nonlinear models of systems such as a glycemic index for diabetic patients, a controller of a Harrier jet and a Pendulum.","abstract_has_math":false,"creators":["Sibai, Hussein Mohamad Ali"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Electrical & Computer Engr","degree_department":null,"school":null,"contributors":["Mitra, Sayan"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-03-13T15:28:45Z","date_published":"2018-03-13T15:28:45Z","updated_at":"2026-07-22T22:24:37Z","subjects":["State estimation","Bit rates","Topological entropy","Switched systems","Nonlinear systems"],"languages":["en"],"rights":["Copyright 2017 Hussein Sibai"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/99265","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mitra, Sayan"]},{"key":"dc:creator","label":"Author","values":["Sibai, Hussein Mohamad Ali"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-03-13T15:28:45Z","2020-03-14T09:15:31Z","2017-12-15","2017-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Electrical & Computer Engr"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"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":["State estimation","Bit rates","Topological entropy","Switched systems","Nonlinear 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 2017 Hussein Sibai"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/99265"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["State estimation is a fundamental problem when monitoring and controlling dynamical systems. Engineering systems interconnect sensing and computing devices over shared bandwidth-limited channels, and therefore, estimation algorithms should strive to use bandwidth optimally. Often, the dynamics of these systems are affected by external factors. In certain cases, these factors would lead the system to switch between different modes. In other cases, they would affect the dynamics of the system continuously in time without leading to explicit mode transitions. In this thesis, we present two notions of entropy for state estimation of nonlinear switched and non-autonomous dynamical systems as lower bounds on the average number of bits needed to be sent from the sensors to the estimators to estimate the states with deterministic (worst case) error bounds. Our approach relies on the notion of topological entropy and uses techniques from control under limited information. Since the computation of these entropies is hard in general, we compute corresponding upper bounds. Additionally, we design a state estimation algorithm for switched systems when their modes cannot be observed. We show that the average bit rate used by the algorithm is optimal in the sense that the efficiency gap is within an additive constant from the gap between the entropy of the considered system and its computed upper-bound. Finally, we apply our theory and algorithms to linear and nonlinear models of systems such as a glycemic index for diabetic patients, a controller of a Harrier jet and a Pendulum.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2019-12-01","The student, Hussein Sibai, accepted the attached license on 2017-12-15 at 15:44.","The student, Hussein Sibai, submitted this Thesis for approval on 2017-12-15 at 15:49.","This Thesis was approved for publication on 2017-12-15 at 16:00.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11998 on 2018-03-13 at 09:58:00","Made available in DSpace on 2018-03-13T15:28:45Z (GMT). No. of bitstreams: 2 SIBAI-THESIS-2017.pdf: 685850 bytes, checksum: 665f514c5b7ff03fa95dfe46673267db (MD5) LICENSE.txt: 4210 bytes, checksum: 28f03afbc2f358f290426af5e2be40d1 (MD5) Previous issue date: 2017-12-15","Embargo set by: Seth Robbins for item 105229 Lift date: 2020-03-13T15:28:52Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 105229 on 2020-03-14T09:15:31Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["State estimation of switched nonlinear systems and systems with bounded inputs: Entropy and bit rates"]}]}],"canonical_facts":{"dc:contributor":["Mitra, Sayan"],"dc:creator":["Sibai, Hussein Mohamad Ali"],"dc:date":["2018-03-13T15:28:45Z","2020-03-14T09:15:31Z","2017-12-15","2017-12"],"dc:description":["State estimation is a fundamental problem when monitoring and controlling dynamical systems. Engineering systems interconnect sensing and computing devices over shared bandwidth-limited channels, and therefore, estimation algorithms should strive to use bandwidth optimally. Often, the dynamics of these systems are affected by external factors. In certain cases, these factors would lead the system to switch between different modes. In other cases, they would affect the dynamics of the system continuously in time without leading to explicit mode transitions. In this thesis, we present two notions of entropy for state estimation of nonlinear switched and non-autonomous dynamical systems as lower bounds on the average number of bits needed to be sent from the sensors to the estimators to estimate the states with deterministic (worst case) error bounds. Our approach relies on the notion of topological entropy and uses techniques from control under limited information. Since the computation of these entropies is hard in general, we compute corresponding upper bounds. Additionally, we design a state estimation algorithm for switched systems when their modes cannot be observed. We show that the average bit rate used by the algorithm is optimal in the sense that the efficiency gap is within an additive constant from the gap between the entropy of the considered system and its computed upper-bound. Finally, we apply our theory and algorithms to linear and nonlinear models of systems such as a glycemic index for diabetic patients, a controller of a Harrier jet and a Pendulum.","Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2019-12-01","The student, Hussein Sibai, accepted the attached license on 2017-12-15 at 15:44.","The student, Hussein Sibai, submitted this Thesis for approval on 2017-12-15 at 15:49.","This Thesis was approved for publication on 2017-12-15 at 16:00.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11998 on 2018-03-13 at 09:58:00","Made available in DSpace on 2018-03-13T15:28:45Z (GMT). No. of bitstreams: 2 SIBAI-THESIS-2017.pdf: 685850 bytes, checksum: 665f514c5b7ff03fa95dfe46673267db (MD5) LICENSE.txt: 4210 bytes, checksum: 28f03afbc2f358f290426af5e2be40d1 (MD5) Previous issue date: 2017-12-15","Embargo set by: Seth Robbins for item 105229 Lift date: 2020-03-13T15:28:52Z Reason: Author requested U of Illinois access only (OA after 2yrs) in Vireo ETD system","U of I Only Restriction Lifted for Item 105229 on 2020-03-14T09:15:31Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/99265"],"dc:language":["en"],"dc:rights":["Copyright 2017 Hussein Sibai"],"dc:subject":["State estimation","Bit rates","Topological entropy","Switched systems","Nonlinear systems"],"dc:title":["State estimation of switched nonlinear systems and systems with bounded inputs: Entropy and bit rates"],"dc:type":["text"],"thesis:degree_discipline":["Electrical & Computer Engr"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["M.S."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:37Z"}