{"id":"https://openalex.org/W2024730047","doi":"https://doi.org/10.1080/10556780600604999","title":"Approximation of reachable sets by direct solution methods for optimal control problems","display_name":"Approximation of reachable sets by direct solution methods for optimal control problems","publication_year":2006,"publication_date":"2006-07-07","ids":{"openalex":"https://openalex.org/W2024730047","doi":"https://doi.org/10.1080/10556780600604999","mag":"2024730047"},"language":"en","primary_location":{"id":"doi:10.1080/10556780600604999","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780600604999","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037003187","display_name":"Robert Baier","orcid":"https://orcid.org/0000-0002-2531-0182"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"R. Baier","raw_affiliation_strings":["Department of Mathematics , University of Bayreuth , D-95440, Bayreuth, Germany","Department of Mathematics, University of Bayreuth, Bayreuth, GERMANY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Bayreuth , D-95440, Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]},{"raw_affiliation_string":"Department of Mathematics, University of Bayreuth, Bayreuth, GERMANY","institution_ids":["https://openalex.org/I54009628"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5024184563","display_name":"Christof B\u00fcskens","orcid":"https://orcid.org/0000-0001-7385-4670"},"institutions":[{"id":"https://openalex.org/I180437899","display_name":"University of Bremen","ror":"https://ror.org/04ers2y35","country_code":"DE","type":"education","lineage":["https://openalex.org/I180437899"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"C. B\u00fcskens","raw_affiliation_strings":["Center for Technomathematics, University of Bremen , Postfach 33 04 40, D-28334, Bremen, Germany","Center for Technomathematics, University of Bremen, Bremen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Technomathematics, University of Bremen , Postfach 33 04 40, D-28334, Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]},{"raw_affiliation_string":"Center for Technomathematics, University of Bremen, Bremen, Germany","institution_ids":["https://openalex.org/I180437899"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049735445","display_name":"Ilyes A\u00efssa Chahma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"I. A. Chahma","raw_affiliation_strings":["Cetelem Bank GmbH , Schwanthalerstra\u00dfe 31, D-80336, M\u00fcnchen, Germany","Cetelem Bank GmbH, M\u00fcnchen, Germany#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Cetelem Bank GmbH , Schwanthalerstra\u00dfe 31, D-80336, M\u00fcnchen, Germany","institution_ids":[]},{"raw_affiliation_string":"Cetelem Bank GmbH, M\u00fcnchen, Germany#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011281312","display_name":"Matthias Gerdts","orcid":"https://orcid.org/0000-0001-8674-5764"},"institutions":[{"id":"https://openalex.org/I159176309","display_name":"Universit\u00e4t Hamburg","ror":"https://ror.org/00g30e956","country_code":"DE","type":"education","lineage":["https://openalex.org/I159176309"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"M. Gerdts","raw_affiliation_strings":["Department of Mathematics , University of Hamburg , Bundesstra\u00dfe 55, D-20146, Hamburg, Germany","Department of Mathematics, University of Hamburg, Hamburg, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Hamburg , Bundesstra\u00dfe 55, D-20146, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]},{"raw_affiliation_string":"Department of Mathematics, University of Hamburg, Hamburg, Germany","institution_ids":["https://openalex.org/I159176309"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011281312"],"corresponding_institution_ids":["https://openalex.org/I159176309"],"apc_list":null,"apc_paid":null,"fwci":1.8225,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.86221226,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"22","issue":"3","first_page":"433","last_page":"452"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9970999956130981,"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":0.9970999956130981,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.9919999837875366,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7735018730163574},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7344334125518799},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.6567889451980591},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.636559009552002},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5528952479362488},{"id":"https://openalex.org/keywords/selection","display_name":"Selection (genetic algorithm)","score":0.5441901683807373},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.4722767770290375},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4653286337852478},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46294888854026794},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4563387930393219},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39606496691703796},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3011355996131897},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18101507425308228},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12158456444740295}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7735018730163574},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7344334125518799},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.6567889451980591},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.636559009552002},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5528952479362488},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.5441901683807373},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.4722767770290375},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4653286337852478},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46294888854026794},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4563387930393219},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39606496691703796},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3011355996131897},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18101507425308228},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12158456444740295},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1080/10556780600604999","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780600604999","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","raw_type":"journal-article"},{"id":"pmh:oai:epub.uni-bayreuth.de:5542","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400362","display_name":"EPub Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:eref.uni-bayreuth.de:63622","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/63622/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Artikel in einer Zeitschrift"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/de564a30-f8fd-4ee2-aafb-f3d9bd8b044e","is_oa":false,"landing_page_url":"https://research.birmingham.ac.uk/en/publications/de564a30-f8fd-4ee2-aafb-f3d9bd8b044e","pdf_url":null,"source":{"id":"https://openalex.org/S4306402634","display_name":"University of Birmingham Research Portal (University of Birmingham)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79619799","host_organization_name":"University of Birmingham","host_organization_lineage":["https://openalex.org/I79619799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Gerdts, M, Baier, R, Buskens, C & Chahma, IA 2007, 'Approximation of reachable sets by direct solution methods for optimal control problems', Optimization Methods and Software, vol. 22, no. 3, pp. 433-452. https://doi.org/10.1080/10556780600604999","raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:epub.uni-bayreuth.de:5542","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400362","display_name":"EPub Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W18120132","https://openalex.org/W90226210","https://openalex.org/W1486936144","https://openalex.org/W1518039036","https://openalex.org/W1530113549","https://openalex.org/W1574393230","https://openalex.org/W1586568018","https://openalex.org/W1597618578","https://openalex.org/W1989810230","https://openalex.org/W1996062108","https://openalex.org/W1999497797","https://openalex.org/W2005411772","https://openalex.org/W2008007187","https://openalex.org/W2018816843","https://openalex.org/W2020254113","https://openalex.org/W2021244475","https://openalex.org/W2031291057","https://openalex.org/W2034647859","https://openalex.org/W2045094421","https://openalex.org/W2047465475","https://openalex.org/W2069394813","https://openalex.org/W2069808690","https://openalex.org/W2070604890","https://openalex.org/W2088176067","https://openalex.org/W2098073114","https://openalex.org/W2098392106","https://openalex.org/W2120276137","https://openalex.org/W2127520982","https://openalex.org/W2163561970","https://openalex.org/W2196589081","https://openalex.org/W2258010296","https://openalex.org/W2433888356","https://openalex.org/W2471629076","https://openalex.org/W2519129372","https://openalex.org/W2529266137","https://openalex.org/W2981569720","https://openalex.org/W3130525865","https://openalex.org/W3134913546","https://openalex.org/W4242576043","https://openalex.org/W4251693851","https://openalex.org/W4293078920"],"related_works":["https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W4206768127","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W4213270568","https://openalex.org/W2334479858","https://openalex.org/W1971388572","https://openalex.org/W2370926798","https://openalex.org/W2898754636"],"abstract_inverted_index":{"A":[0],"numerical":[1],"method":[2,16,62,88],"for":[3,50,70],"the":[4,20,46,51,56,60,66,77,104,109],"approximation":[5,49],"of":[6,9,22,48,59,80,111],"reachable":[7,52],"sets":[8],"linear":[10],"control":[11,25,71],"systems":[12],"is":[13,17,89,113],"discussed.":[14],"The":[15,87],"based":[18],"on":[19,55],"formulation":[21],"suitable":[23],"optimal":[24],"problems":[26],"with":[27,65,118],"varying":[28],"objective":[29],"function,":[30],"whose":[31],"discretization":[32],"by":[33,91],"Runge\u2013Kutta":[34,61,97],"methods":[35,98],"leads":[36],"to":[37],"finite-dimensional":[38],"convex":[39],"optimization":[40],"problems.":[41],"It":[42],"turns":[43],"out":[44],"that":[45],"order":[47,79,110],"set":[53],"depends":[54],"particular":[57],"choice":[58],"in":[63,85,102,121],"combination":[64],"selection":[67,100],"strategy":[68],"used":[69],"approximation.":[72],"For":[73],"an":[74],"inappropriate":[75],"combination,":[76],"expected":[78],"convergence":[81,112],"cannot":[82],"be":[83],"achieved":[84],"general.":[86],"illustrated":[90],"two":[92],"test":[93],"examples":[94],"using":[95],"different":[96],"and":[99,116],"strategies,":[101],"which":[103],"run":[105],"times":[106],"are":[107],"analysed,":[108],"estimated":[114],"numerically":[115],"compared":[117],"theoretical":[119],"results":[120],"similar":[122],"areas.":[123]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}