{"id":"https://openalex.org/W4280592041","doi":"https://doi.org/10.3390/axioms11050214","title":"Cheap Control in a Non-Scalarizable Linear-Quadratic Pursuit-Evasion Game: Asymptotic Analysis","display_name":"Cheap Control in a Non-Scalarizable Linear-Quadratic Pursuit-Evasion Game: Asymptotic Analysis","publication_year":2022,"publication_date":"2022-05-05","ids":{"openalex":"https://openalex.org/W4280592041","doi":"https://doi.org/10.3390/axioms11050214"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11050214","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050214","pdf_url":"https://www.mdpi.com/2075-1680/11/5/214/pdf?version=1651750166","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/5/214/pdf?version=1651750166","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038274765","display_name":"Vladimir Turetsky","orcid":"https://orcid.org/0000-0002-9385-7999"},"institutions":[{"id":"https://openalex.org/I231622532","display_name":"ORT Braude College","ror":"https://ror.org/004af2v94","country_code":"IL","type":"education","lineage":["https://openalex.org/I231622532"]}],"countries":["IL"],"is_corresponding":true,"raw_author_name":"Vladimir Turetsky","raw_affiliation_strings":["Department of Mathematics, Ort Braude College of Engineering, 51 Snunit Str., P.O. Box 78, Karmiel 2161002, Israel"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ort Braude College of Engineering, 51 Snunit Str., P.O. Box 78, Karmiel 2161002, Israel","institution_ids":["https://openalex.org/I231622532"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5055174523","display_name":"Valery Y. Glizer","orcid":"https://orcid.org/0000-0002-8877-5008"},"institutions":[{"id":"https://openalex.org/I231622532","display_name":"ORT Braude College","ror":"https://ror.org/004af2v94","country_code":"IL","type":"education","lineage":["https://openalex.org/I231622532"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Valery Glizer","raw_affiliation_strings":["The Galilee Research Center for Applied Mathematics, Ort Braude College of Engineering, 51 Snunit Str., P.O. Box 78, Karmiel 2161002, Israel"],"affiliations":[{"raw_affiliation_string":"The Galilee Research Center for Applied Mathematics, Ort Braude College of Engineering, 51 Snunit Str., P.O. Box 78, Karmiel 2161002, Israel","institution_ids":["https://openalex.org/I231622532"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5038274765"],"corresponding_institution_ids":["https://openalex.org/I231622532"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.5394,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.84904098,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"11","issue":"5","first_page":"214","last_page":"214"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12158","display_name":"Guidance and Control Systems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T12158","display_name":"Guidance and Control Systems","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace 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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9652000069618225,"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/differential-game","display_name":"Differential game","score":0.7961764335632324},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6896427273750305},{"id":"https://openalex.org/keywords/example-of-a-game-without-a-value","display_name":"Example of a game without a value","score":0.6741617321968079},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5245454907417297},{"id":"https://openalex.org/keywords/sequential-game","display_name":"Sequential game","score":0.5020096302032471},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4867117702960968},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.4268595576286316},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4037555754184723},{"id":"https://openalex.org/keywords/normal-form-game","display_name":"Normal-form game","score":0.3705641031265259},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34415000677108765},{"id":"https://openalex.org/keywords/game-theory","display_name":"Game theory","score":0.3269529342651367},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.30709943175315857}],"concepts":[{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.7961764335632324},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6896427273750305},{"id":"https://openalex.org/C138328387","wikidata":"https://www.wikidata.org/wiki/Q5419308","display_name":"Example of a game without a value","level":5,"score":0.6741617321968079},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5245454907417297},{"id":"https://openalex.org/C73795354","wikidata":"https://www.wikidata.org/wiki/Q287618","display_name":"Sequential game","level":3,"score":0.5020096302032471},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4867117702960968},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.4268595576286316},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4037555754184723},{"id":"https://openalex.org/C155930848","wikidata":"https://www.wikidata.org/wiki/Q1069099","display_name":"Normal-form game","level":4,"score":0.3705641031265259},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34415000677108765},{"id":"https://openalex.org/C177142836","wikidata":"https://www.wikidata.org/wiki/Q44455","display_name":"Game theory","level":2,"score":0.3269529342651367},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.30709943175315857},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11050214","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050214","pdf_url":"https://www.mdpi.com/2075-1680/11/5/214/pdf?version=1651750166","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:c0f9d8d61fba4948a8e7cb0d5a068e06","is_oa":true,"landing_page_url":"https://doaj.org/article/c0f9d8d61fba4948a8e7cb0d5a068e06","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 5, p 214 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/5/214/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11050214","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 5; Pages: 214","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11050214","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11050214","pdf_url":"https://www.mdpi.com/2075-1680/11/5/214/pdf?version=1651750166","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280592041.pdf","grobid_xml":"https://content.openalex.org/works/W4280592041.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1532777065","https://openalex.org/W1547240457","https://openalex.org/W2012524581","https://openalex.org/W2018601820","https://openalex.org/W2018839384","https://openalex.org/W2019444629","https://openalex.org/W2040238231","https://openalex.org/W2040499356","https://openalex.org/W2042917674","https://openalex.org/W2049287102","https://openalex.org/W2060228235","https://openalex.org/W2068973607","https://openalex.org/W2079179009","https://openalex.org/W2082745938","https://openalex.org/W2122821164","https://openalex.org/W2141784777","https://openalex.org/W2163839133","https://openalex.org/W2318104318","https://openalex.org/W3035578948","https://openalex.org/W4239184375","https://openalex.org/W6780383567"],"related_works":["https://openalex.org/W4321497886","https://openalex.org/W651698058","https://openalex.org/W2056920506","https://openalex.org/W4300767433","https://openalex.org/W2949228172","https://openalex.org/W1994742051","https://openalex.org/W2518385624","https://openalex.org/W2046396881","https://openalex.org/W2884690177","https://openalex.org/W3175059945"],"abstract_inverted_index":{"In":[0,15],"this":[1],"work,":[2],"a":[3,10,60],"finite-horizon":[4],"zero-sum":[5],"linear-quadratic":[6],"differential":[7],"game,":[8],"modeling":[9],"pursuit-evasion":[11],"problem,":[12],"was":[13,32,57,133,144,160,175],"considered.":[14],"the":[16,20,23,26,36,39,42,49,52,68,71,74,78,85,88,97,107,116,120,124,129,141,151,157,163,168],"game\u2019s":[17,89,131],"cost":[18,21,37,50,79,172],"function,":[19],"of":[22,25,38,41,51,67,70,73,87,106,119,123,150],"control":[24,40,76,154,171],"minimizing":[27],"player":[28,44],"(the":[29,45,91],"minimizer/the":[30],"pursuer)":[31],"much":[33],"smaller":[34],"than":[35],"maximizing":[43],"maximizer/the":[46],"evader)":[47],"and":[48,96,156],"state":[53],"variable.":[54],"This":[55],"smallness":[56],"expressed":[58],"by":[59,166],"positive":[61],"small":[62,65,104,117,169],"multiplier":[63],"(a":[64],"parameter)":[66,118],"square":[69],"L2-norm":[72],"minimizer\u2019s":[75,142,170],"in":[77],"function.":[80],"Parameter-free":[81],"sufficient":[82],"conditions":[83],"for":[84,101],"existence":[86],"solution":[90],"players\u2019":[92],"optimal":[93,125],"state-feedback":[94,126],"controls":[95,127],"game":[98,138,155,158],"value),":[99],"valid":[100],"all":[102],"sufficiently":[103],"values":[105],"parameter,":[108],"were":[109],"presented.":[110,182],"The":[111,135],"boundedness":[112],"(with":[113],"respect":[114],"to":[115],"time":[121],"realizations":[122],"along":[128],"corresponding":[130],"trajectory":[132],"established.":[134,176],"best":[136],"achievable":[137],"value":[139],"from":[140,162],"viewpoint":[143],"derived.":[145],"A":[146],"relation":[147],"between":[148],"solutions":[149],"original":[152,164],"cheap":[153],"that":[159],"obtained":[161],"one":[165],"replacing":[167],"with":[173],"zero,":[174],"An":[177],"illustrative":[178],"real-life":[179],"example":[180],"is":[181]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-05-22T00:00:00"}
