{"id":"https://openalex.org/W2051653155","doi":"https://doi.org/10.1137/040618072","title":"Hybrid Control Systems and Viscosity Solutions","display_name":"Hybrid Control Systems and Viscosity Solutions","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2051653155","doi":"https://doi.org/10.1137/040618072","mag":"2051653155"},"language":"en","primary_location":{"id":"doi:10.1137/040618072","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040618072","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029512188","display_name":"Sheetal Dharmatti","orcid":"https://orcid.org/0000-0001-7011-4108"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sheetal Dharmatti","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5031302510","display_name":"Mythily Ramaswamy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mythily Ramaswamy","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9931,"has_fulltext":false,"cited_by_count":61,"citation_normalized_percentile":{"value":0.91453576,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"4","first_page":"1259","last_page":"1288"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9761999845504761,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11072","display_name":"Peroxisome Proliferator-Activated Receptors","score":0.9314000010490417,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8194539546966553},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.7273149490356445},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.5915354490280151},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5831841230392456},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.5767650008201599},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.5033861994743347},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4900568723678589},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.47904694080352783},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.47742876410484314},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.4428026080131531},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42302805185317993},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4197568893432617},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4195590019226074},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36658066511154175},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.30459895730018616},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.27724283933639526},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12416523694992065},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08416754007339478}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8194539546966553},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.7273149490356445},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.5915354490280151},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5831841230392456},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.5767650008201599},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.5033861994743347},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4900568723678589},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.47904694080352783},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.47742876410484314},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.4428026080131531},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42302805185317993},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4197568893432617},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4195590019226074},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36658066511154175},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.30459895730018616},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27724283933639526},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12416523694992065},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08416754007339478},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/040618072","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040618072","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:eprints.iisc.ac.in:4790","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4377196309","display_name":"NOT FOUND REPOSITORY (Indian Institute of Science Bangalore)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I59270414","host_organization_name":"Indian Institute of Science Bangalore","host_organization_lineage":["https://openalex.org/I59270414"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.607.93","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.607.93","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://math.tifrbng.res.in/~mythily/file_ps/sd-mr-siam.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.5}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":8,"referenced_works":["https://openalex.org/W1487586009","https://openalex.org/W1550227333","https://openalex.org/W1981323954","https://openalex.org/W1986504609","https://openalex.org/W1989022272","https://openalex.org/W2098916117","https://openalex.org/W2152185829","https://openalex.org/W2593901252"],"related_works":["https://openalex.org/W2766367749","https://openalex.org/W4287078947","https://openalex.org/W1654696814","https://openalex.org/W4297940580","https://openalex.org/W2954291171","https://openalex.org/W4297409026","https://openalex.org/W2088353628","https://openalex.org/W2313187187","https://openalex.org/W2032834442","https://openalex.org/W3153900688"],"abstract_inverted_index":{"We":[0,78,114],"investigate":[1],"a":[2,27,52,74,104],"model":[3],"of":[4,33,82,125],"hybrid":[5],"control":[6],"system":[7,25,35],"inwhich":[8],"both":[9],"discrete":[10,20],"and":[11],"continuous":[12],"controls":[13,21],"are":[14],"involved.":[15],"In":[16],"this":[17],"general":[18],"model,":[19],"act":[22],"on":[23],"the":[24,34,40,58,69,80,83,91,95,111,116,121,126,130],"at":[26],"given":[28],"set":[29,49,55],"interface.":[30],"The":[31],"state":[32],"is":[36],"changed":[37],"discontinuously":[38],"when":[39],"trajectory":[41,70],"hits":[42],"predefined":[43],"sets,":[44],"namely,":[45],"an":[46],"autonomous":[47],"jump":[48,54,63],"A":[50],"or":[51,64],"controlled":[53],"C":[56],"where":[57],"controller":[59],"can":[60,71],"choose":[61],"to":[62,73,90],"not.":[65],"At":[66],"each":[67],"jump,":[68],"move":[72],"different":[75],"Euclidean":[76],"space.":[77],"prove":[79],"continuity":[81],"associated":[84],"value":[85,117],"function":[86,118],"V":[87,109,119],"with":[88],"respect":[89],"initial":[92],"point.":[93],"Using":[94],"dynamic":[96],"programming":[97],"principle":[98,132],"satisfied":[99,107],"by":[100,108,129],"V,":[101],"we":[102],"derive":[103],"quasi-variational":[105,127],"inequality":[106,128],"in":[110],"viscosity":[112,123],"sense.":[113],"characterize":[115],"as":[120],"unique":[122],"solution":[124],"comparison":[131],"method.":[133]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}