{"id":"https://openalex.org/W2072882105","doi":"https://doi.org/10.1007/s10626-011-0123-x","title":"Modeling and control of switching max-plus-linear systems with random and deterministic switching","display_name":"Modeling and control of switching max-plus-linear systems with random and deterministic switching","publication_year":2011,"publication_date":"2011-12-06","ids":{"openalex":"https://openalex.org/W2072882105","doi":"https://doi.org/10.1007/s10626-011-0123-x","mag":"2072882105"},"language":"en","primary_location":{"id":"doi:10.1007/s10626-011-0123-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10626-011-0123-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10626-011-0123-x.pdf","source":{"id":"https://openalex.org/S134484881","display_name":"Discrete Event Dynamic Systems","issn_l":"0924-6703","issn":["0924-6703","1573-7594"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Event Dynamic Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10626-011-0123-x.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027927390","display_name":"Ton van den Boom","orcid":"https://orcid.org/0000-0002-3752-8859"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Ton J. J. van den Boom","raw_affiliation_strings":["Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628, CD Delft, The Netherlands","Delft Center for Systems and Control, Delft University of Technology, CD Delft , The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628, CD Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, CD Delft , The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026547410","display_name":"Bart De Schutter","orcid":"https://orcid.org/0000-0001-9867-6196"},"institutions":[{"id":"https://openalex.org/I98358874","display_name":"Delft University of Technology","ror":"https://ror.org/02e2c7k09","country_code":"NL","type":"education","lineage":["https://openalex.org/I98358874"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Bart De Schutter","raw_affiliation_strings":["Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628, CD Delft, The Netherlands","Delft Center for Systems and Control, Delft University of Technology, CD Delft , The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628, CD Delft, The Netherlands","institution_ids":["https://openalex.org/I98358874"]},{"raw_affiliation_string":"Delft Center for Systems and Control, Delft University of Technology, CD Delft , The Netherlands","institution_ids":["https://openalex.org/I98358874"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5027927390"],"corresponding_institution_ids":["https://openalex.org/I98358874"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":2.7498,"has_fulltext":true,"cited_by_count":33,"citation_normalized_percentile":{"value":0.91914832,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"3","first_page":"293","last_page":"332"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11125","display_name":"Petri Nets in System Modeling","score":0.9984999895095825,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9947999715805054,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.6241894960403442},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5925728678703308},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5858299732208252},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.5597450733184814},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5376890897750854},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5066707730293274},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4963439106941223},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.49169307947158813},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.43776246905326843},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4357207417488098},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33230215311050415},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3249010741710663},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.24486380815505981}],"concepts":[{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.6241894960403442},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5925728678703308},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5858299732208252},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.5597450733184814},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5376890897750854},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5066707730293274},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4963439106941223},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.49169307947158813},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.43776246905326843},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4357207417488098},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33230215311050415},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3249010741710663},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.24486380815505981},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10626-011-0123-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10626-011-0123-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10626-011-0123-x.pdf","source":{"id":"https://openalex.org/S134484881","display_name":"Discrete Event Dynamic Systems","issn_l":"0924-6703","issn":["0924-6703","1573-7594"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Event Dynamic Systems","raw_type":"journal-article"},{"id":"pmh:oai:tudelft.nl:uuid:1bd7bf80-4b1d-4bd5-b453-3286cb45bb08","is_oa":false,"landing_page_url":"http://resolver.tudelft.nl/uuid:1bd7bf80-4b1d-4bd5-b453-3286cb45bb08","pdf_url":null,"source":{"id":"https://openalex.org/S4306400906","display_name":"Research Repository (Delft University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I98358874","host_organization_name":"Delft University of Technology","host_organization_lineage":["https://openalex.org/I98358874"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.1007/s10626-011-0123-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10626-011-0123-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10626-011-0123-x.pdf","source":{"id":"https://openalex.org/S134484881","display_name":"Discrete Event Dynamic Systems","issn_l":"0924-6703","issn":["0924-6703","1573-7594"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Event Dynamic Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334893","display_name":"Stichting voor de Technische Wetenschappen","ror":"https://ror.org/057tq3593"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2072882105.pdf","grobid_xml":"https://content.openalex.org/works/W2072882105.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W124292005","https://openalex.org/W573996599","https://openalex.org/W1237856907","https://openalex.org/W1506932277","https://openalex.org/W1539140425","https://openalex.org/W1541170979","https://openalex.org/W1561941139","https://openalex.org/W1576823098","https://openalex.org/W1582020666","https://openalex.org/W1584148765","https://openalex.org/W1587663028","https://openalex.org/W1587861032","https://openalex.org/W1592497244","https://openalex.org/W1631623342","https://openalex.org/W1855336155","https://openalex.org/W1963902882","https://openalex.org/W1964585380","https://openalex.org/W1965663154","https://openalex.org/W1969308522","https://openalex.org/W1977985274","https://openalex.org/W1984854829","https://openalex.org/W1985662530","https://openalex.org/W1994188141","https://openalex.org/W1999856942","https://openalex.org/W2010823926","https://openalex.org/W2014337138","https://openalex.org/W2023599497","https://openalex.org/W2033040247","https://openalex.org/W2049512840","https://openalex.org/W2053862301","https://openalex.org/W2072508748","https://openalex.org/W2085613095","https://openalex.org/W2091683987","https://openalex.org/W2101603248","https://openalex.org/W2102098378","https://openalex.org/W2102260333","https://openalex.org/W2105469716","https://openalex.org/W2123848193","https://openalex.org/W2125603090","https://openalex.org/W2140007372","https://openalex.org/W2155795362","https://openalex.org/W2157249226","https://openalex.org/W2157801723","https://openalex.org/W2166843422","https://openalex.org/W2169097986","https://openalex.org/W2213594914","https://openalex.org/W2339500526","https://openalex.org/W2613020344","https://openalex.org/W3103254642","https://openalex.org/W3140305187","https://openalex.org/W3203995261","https://openalex.org/W4212899374","https://openalex.org/W4241496298","https://openalex.org/W4297744580"],"related_works":["https://openalex.org/W3173321515","https://openalex.org/W2743650898","https://openalex.org/W2369734084","https://openalex.org/W2007464938","https://openalex.org/W2784100870","https://openalex.org/W2354774539","https://openalex.org/W1972615387","https://openalex.org/W2111110449","https://openalex.org/W3123050985","https://openalex.org/W2064873618"],"abstract_inverted_index":{"Switching":[0],"max-plus-linear":[1,24,29,64,76],"(SMPL)":[2],"systems":[3,6,65,122],"are":[4,161],"discrete-event":[5],"that":[7,73,170],"can":[8,78,95,181],"switch":[9],"between":[10],"different":[11,33],"modes":[12],"of":[13,106,167],"operation.":[14],"In":[15,56,128],"each":[16,37],"mode":[17,175],"the":[18,44,47,104,107,110,130,133,148,158,165,173,177],"system":[19,34,77,85],"is":[20,151],"described":[21],"by":[22],"a":[23,28,53,74,82,88,115,142],"state":[25],"equation":[26],"and":[27,46,109,157],"output":[30],"equation,":[31],"with":[32,123],"matrices":[35],"for":[36,62,120],"mode.":[38],"The":[39,92],"switching":[40,63,75,169],"may":[41,51],"depend":[42],"on":[43,103,154,172],"inputs":[45],"states,":[48],"or":[49,86],"it":[50],"be":[52,67,79,96,182],"stochastic":[54,126,168],"process.":[55],"this":[57],"paper":[58],"two":[59],"equivalent":[60],"descriptions":[61],"will":[66,70],"discussed.":[68],"We":[69,112],"also":[71,113],"show":[72],"written":[80],"as":[81,87],"piecewise":[83,152],"affine":[84],"constrained":[89],"max-min-plus-scaling":[90],"system.":[91],"last":[93],"translation":[94],"established":[97],"under":[98],"(rather":[99],"mild)":[100],"additional":[101],"assumptions":[102],"boundedness":[105],"states":[108],"inputs.":[111],"develop":[114],"stabilizing":[116],"model":[117,134],"predictive":[118,135],"controller":[119],"SMPL":[121],"deterministic":[124],"and/or":[125],"switching.":[127],"general,":[129],"optimization":[131,145,179],"in":[132,164],"control":[136],"approach":[137],"then":[138],"boils":[139],"down":[140],"to":[141],"nonlinear":[143],"nonconvex":[144],"problem,":[146],"where":[147],"cost":[149],"criterion":[150],"polynomial":[153],"polyhedral":[155],"sets":[156],"inequality":[159],"constraints":[160],"linear.":[162],"However,":[163],"case":[166],"depends":[171],"previous":[174],"only,":[176],"resulting":[178],"problem":[180],"solved":[183],"using":[184],"linear":[185],"programming":[186],"algorithms.":[187]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
