{"id":"https://openalex.org/W3090724729","doi":"https://doi.org/10.1134/s0005117920080159","title":"A Numerical Method for Solving Time-Optimal Differential Games with a Lifeline","display_name":"A Numerical Method for Solving Time-Optimal Differential Games with a Lifeline","publication_year":2020,"publication_date":"2020-08-01","ids":{"openalex":"https://openalex.org/W3090724729","doi":"https://doi.org/10.1134/s0005117920080159","mag":"3090724729"},"language":"en","primary_location":{"id":"doi:10.1134/s0005117920080159","is_oa":true,"landing_page_url":"https://doi.org/10.1134/s0005117920080159","pdf_url":"https://link.springer.com/content/pdf/10.1134/S0005117920080159.pdf","source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1134/S0005117920080159.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063774059","display_name":"Nataly V. Munts","orcid":"https://orcid.org/0000-0003-3234-1267"},"institutions":[{"id":"https://openalex.org/I4210105350","display_name":"N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences","ror":"https://ror.org/029fhmb28","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210105350","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"N.V. Munts","raw_affiliation_strings":["Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Saint Petersburg, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I4210105350"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049262508","display_name":"Sergey S. Kumkov","orcid":"https://orcid.org/0000-0002-2690-5380"},"institutions":[{"id":"https://openalex.org/I4210105350","display_name":"N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences","ror":"https://ror.org/029fhmb28","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210105350","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"S.S. Kumkov","raw_affiliation_strings":["Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Saint Petersburg, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Krasovskii Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I4210105350"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210105350"],"apc_list":null,"apc_paid":null,"fwci":0.8288,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.79362319,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"81","issue":"8","first_page":"1545","last_page":"1561"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9927999973297119,"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":0.9927999973297119,"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/T12158","display_name":"Guidance and Control Systems","score":0.9909999966621399,"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/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.9847000241279602,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.65456223487854},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6453624367713928},{"id":"https://openalex.org/keywords/viscosity-solution","display_name":"Viscosity solution","score":0.5658994913101196},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5522522330284119},{"id":"https://openalex.org/keywords/differential-game","display_name":"Differential game","score":0.5460415482521057},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5292893052101135},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.49770596623420715},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4848417043685913},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.46314120292663574},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4626399576663971},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4360445737838745},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.41792070865631104},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.41519105434417725},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.41366660594940186},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32650795578956604},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.15589645504951477},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14170902967453003},{"id":"https://openalex.org/keywords/aerospace-engineering","display_name":"Aerospace engineering","score":0.07841178774833679}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.65456223487854},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6453624367713928},{"id":"https://openalex.org/C88731125","wikidata":"https://www.wikidata.org/wiki/Q7935676","display_name":"Viscosity solution","level":2,"score":0.5658994913101196},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5522522330284119},{"id":"https://openalex.org/C2779006483","wikidata":"https://www.wikidata.org/wiki/Q1973196","display_name":"Differential game","level":2,"score":0.5460415482521057},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5292893052101135},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.49770596623420715},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4848417043685913},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.46314120292663574},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4626399576663971},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4360445737838745},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.41792070865631104},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.41519105434417725},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41366660594940186},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32650795578956604},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.15589645504951477},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14170902967453003},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.07841178774833679},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1134/s0005117920080159","is_oa":true,"landing_page_url":"https://doi.org/10.1134/s0005117920080159","pdf_url":"https://link.springer.com/content/pdf/10.1134/S0005117920080159.pdf","source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1134/s0005117920080159","is_oa":true,"landing_page_url":"https://doi.org/10.1134/s0005117920080159","pdf_url":"https://link.springer.com/content/pdf/10.1134/S0005117920080159.pdf","source":{"id":"https://openalex.org/S134188425","display_name":"Automation and Remote Control","issn_l":"0005-1179","issn":["0005-1179","1608-3032"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320267","host_organization_name":"Pleiades Publishing","host_organization_lineage":["https://openalex.org/P4310320267","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Pleiades Publishing","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Automation and Remote Control","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1148188478","display_name":null,"funder_award_id":"18-01-","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"},{"id":"https://openalex.org/G6976133432","display_name":null,"funder_award_id":"18-01-00410","funder_id":"https://openalex.org/F4320321079","funder_display_name":"Russian Foundation for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3090724729.pdf","grobid_xml":"https://content.openalex.org/works/W3090724729.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W77519437","https://openalex.org/W130364825","https://openalex.org/W1487586009","https://openalex.org/W1505284970","https://openalex.org/W1547240457","https://openalex.org/W1552025512","https://openalex.org/W1581842928","https://openalex.org/W1605799302","https://openalex.org/W1879112630","https://openalex.org/W1968070254","https://openalex.org/W2032316144","https://openalex.org/W2041857090","https://openalex.org/W2056616297","https://openalex.org/W2057462050","https://openalex.org/W2275013148","https://openalex.org/W2492012602","https://openalex.org/W2888914392","https://openalex.org/W2980527142"],"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/W2950973671","https://openalex.org/W3124904228"],"abstract_inverted_index":{"Time-optimal":[0],"differential":[1],"games":[2,56],"with":[3,57],"a":[4,26,58,71],"lifeline":[5,59],"are":[6,12],"considered.":[7],"In":[8],"such":[9],"games,":[10],"there":[11],"two":[13],"sets":[14],"of":[15,85],"interest:":[16],"the":[17,23,34,42,48,65,75,80,86],"first":[18],"player":[19,36],"tries":[20],"to":[21,74],"guide":[22],"system":[24,43],"into":[25],"target":[27],"set":[28,46],"as":[29,31,70],"soon":[30],"possible,":[32],"while":[33],"second":[35],"counteracts":[37],"him":[38],"and":[39],"wins":[40],"if":[41],"reaches":[44],"another":[45],"(called":[47],"lifeline).":[49],"A":[50],"numerical":[51],"method":[52,87],"for":[53,79],"solving":[54],"time-optimal":[55],"is":[60,68,88],"suggested.":[61],"With":[62],"this":[63],"method,":[64],"value":[66],"function":[67],"designed":[69],"viscosity":[72],"solution":[73],"corresponding":[76],"boundary-value":[77],"problem":[78],"Hamilton\u2013Jacobi":[81],"equation.":[82],"The":[83],"convergence":[84],"established.":[89]},"counts_by_year":[{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}