{"id":"https://openalex.org/W2012186120","doi":"https://doi.org/10.1109/tcst.2012.2190935","title":"Implementation of Dynamic Programming for $n$-Dimensional Optimal Control Problems With Final State Constraints","display_name":"Implementation of Dynamic Programming for $n$-Dimensional Optimal Control Problems With Final State Constraints","publication_year":2012,"publication_date":"2012-04-04","ids":{"openalex":"https://openalex.org/W2012186120","doi":"https://doi.org/10.1109/tcst.2012.2190935","mag":"2012186120"},"language":"en","primary_location":{"id":"doi:10.1109/tcst.2012.2190935","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2012.2190935","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Control Systems Technology","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/A5108200568","display_name":"Philipp Elbert","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Philipp Elbert","raw_affiliation_strings":["Department of Mechanical and Process Engineering, ETH Z\u00fcrich, Zurich, Switzerland","Dept. of Mech. & Process Eng, ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Process Engineering, ETH Z\u00fcrich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Dept. of Mech. & Process Eng, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073646286","display_name":"S\u00f8ren Ebbesen","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Soren Ebbesen","raw_affiliation_strings":["Department of Mechanical and Process Engineering, ETH Z\u00fcrich, Zurich, Switzerland","Dept. of Mech. & Process Eng, ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Process Engineering, ETH Z\u00fcrich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Dept. of Mech. & Process Eng, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056073231","display_name":"Lino Guzzella","orcid":"https://orcid.org/0000-0002-8781-3199"},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Lino Guzzella","raw_affiliation_strings":["Department of Mechanical and Process Engineering, ETH Z\u00fcrich, Zurich, Switzerland","Dept. of Mech. & Process Eng, ETH Zurich, Zurich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and Process Engineering, ETH Z\u00fcrich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"Dept. of Mech. & Process Eng, ETH Zurich, Zurich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.9881,"has_fulltext":false,"cited_by_count":171,"citation_normalized_percentile":{"value":0.97973811,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"21","issue":"3","first_page":"924","last_page":"931"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9987999796867371,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9987999796867371,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9668999910354614,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9115999937057495,"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/discretization","display_name":"Discretization","score":0.8702647089958191},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.7244676351547241},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6688065528869629},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.6457041501998901},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.5716648101806641},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5713202953338623},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5673402547836304},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4869016706943512},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47754108905792236},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.47265684604644775},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.44850364327430725},{"id":"https://openalex.org/keywords/discretization-of-continuous-features","display_name":"Discretization of continuous features","score":0.42175763845443726},{"id":"https://openalex.org/keywords/nonlinear-programming","display_name":"Nonlinear programming","score":0.41297584772109985},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39473193883895874},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3842692971229553},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.37965530157089233},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.33132633566856384},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.18860268592834473}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8702647089958191},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.7244676351547241},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6688065528869629},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.6457041501998901},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.5716648101806641},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5713202953338623},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5673402547836304},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4869016706943512},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47754108905792236},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.47265684604644775},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.44850364327430725},{"id":"https://openalex.org/C105427703","wikidata":"https://www.wikidata.org/wiki/Q665193","display_name":"Discretization of continuous features","level":4,"score":0.42175763845443726},{"id":"https://openalex.org/C115527620","wikidata":"https://www.wikidata.org/wiki/Q769909","display_name":"Nonlinear programming","level":3,"score":0.41297584772109985},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39473193883895874},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3842692971229553},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.37965530157089233},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33132633566856384},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.18860268592834473},{"id":"https://openalex.org/C126148662","wikidata":"https://www.wikidata.org/wiki/Q3890355","display_name":"Discretization error","level":3,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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":1,"locations":[{"id":"doi:10.1109/tcst.2012.2190935","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2012.2190935","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Control Systems Technology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/17","display_name":"Partnerships for the goals","score":0.4099999964237213}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W104496005","https://openalex.org/W1512691241","https://openalex.org/W1586568018","https://openalex.org/W1941445455","https://openalex.org/W2002971752","https://openalex.org/W2035407117","https://openalex.org/W2050838777","https://openalex.org/W2098432798","https://openalex.org/W2102158516","https://openalex.org/W2152938561","https://openalex.org/W2487144912","https://openalex.org/W4299935191","https://openalex.org/W6604323055","https://openalex.org/W6634908830"],"related_works":["https://openalex.org/W4285537323","https://openalex.org/W2379312070","https://openalex.org/W2136173754","https://openalex.org/W2332086753","https://openalex.org/W2953025626","https://openalex.org/W2499081552","https://openalex.org/W2110050003","https://openalex.org/W2366053282","https://openalex.org/W2107074475","https://openalex.org/W345900361"],"abstract_inverted_index":{"Many":[0],"optimal":[1,203],"control":[2,12,204],"problems":[3,173],"include":[4],"a":[5,25,125,150,169,187,218],"continuous":[6],"nonlinear":[7],"dynamic":[8,20],"system,":[9],"state,":[10],"and":[11,14,35,70],"constraints,":[13],"final":[15,111,120],"state":[16,112],"constraints.":[17],"When":[18,48],"using":[19],"programming":[21],"to":[22,32,39,56,92,128,149,156,168,176],"solve":[23],"such":[24,50],"problem,":[26],"the":[27,41,45,62,65,79,88,94,100,105,110,118,141,177,180,184,195,209,212,224,227],"solution":[28,67,228],"space":[29,107],"typically":[30],"needs":[31],"be":[33,74,115],"discretized":[34],"interpolation":[36],"is":[37,54,99,132,146,206],"used":[38],"evaluate":[40],"cost-to-go":[42],"function":[43],"between":[44],"grid":[46],"points.":[47],"implementing":[49],"an":[51,199,201],"algorithm,":[52],"it":[53,145],"important":[55],"treat":[57],"numerical":[58],"issues":[59],"appropriately.":[60],"Otherwise,":[61],"accuracy":[63,225],"of":[64,81,102,140,153,172,186,191,220,226],"found":[66,142],"will":[68,85],"deteriorate":[69],"global":[71,138,163],"optimality":[72,139,164],"can":[73],"restored":[75],"only":[76],"by":[77,217],"increasing":[78],"level":[80,190],"discretization.":[82],"Unfortunately,":[83],"this":[84,123,130],"also":[86],"increase":[87],"computational":[89],"effort":[90],"needed":[91],"calculate":[93],"solution.":[95],"A":[96],"known":[97],"problem":[98,131,205],"treatment":[101],"states":[103],"in":[104],"time\u2013state":[106],"from":[108],"which":[109],"constraint":[113],"cannot":[114],"met":[116],"within":[117],"given":[119],"time.":[121],"In":[122],"brief,":[124],"novel":[126],"method":[127,136,182],"handle":[129],"presented.":[133],"The":[134],"new":[135,210],"guarantees":[137],"solution,":[143],"while":[144,193,223],"not":[147],"restricted":[148],"specific":[151,170],"class":[152,171],"problems.":[154],"Opposed":[155],"that,":[157],"previously":[158],"proposed":[159,181],"methods":[160],"either":[161],"sacrifice":[162],"or":[165],"are":[166],"applicable":[167],"only.":[174],"Compared":[175],"basic":[178],"implementation,":[179],"allows":[183],"use":[185],"substantially":[188],"lower":[189],"discretization":[192],"achieving":[194],"same":[196],"accuracy.":[197],"As":[198],"example,":[200],"academic":[202],"analyzed.":[207],"With":[208],"method,":[211],"evaluation":[213],"time":[214],"was":[215,229],"reduced":[216],"factor":[219],"about":[221],"300,":[222],"maintained.":[230]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":23},{"year":2021,"cited_by_count":18},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":20},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":16},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":14},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
