{"id":"https://openalex.org/W3177642153","doi":"https://doi.org/10.1109/tvt.2021.3075729","title":"Fuel Minimization of a Hybrid Electric Racing Car by Quasi-Pontryagin's Minimum Principle","display_name":"Fuel Minimization of a Hybrid Electric Racing Car by Quasi-Pontryagin's Minimum Principle","publication_year":2021,"publication_date":"2021-04-27","ids":{"openalex":"https://openalex.org/W3177642153","doi":"https://doi.org/10.1109/tvt.2021.3075729","mag":"3177642153"},"language":"en","primary_location":{"id":"doi:10.1109/tvt.2021.3075729","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tvt.2021.3075729","pdf_url":"https://ieeexplore.ieee.org/ielx7/25/9477511/09416826.pdf","source":{"id":"https://openalex.org/S10936095","display_name":"IEEE Transactions on Vehicular Technology","issn_l":"0018-9545","issn":["0018-9545","1939-9359"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Vehicular Technology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://ieeexplore.ieee.org/ielx7/25/9477511/09416826.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100392629","display_name":"Tong Liu","orcid":"https://orcid.org/0000-0001-9556-6856"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Tong Liu","raw_affiliation_strings":["Department of Machine Design, KTH Royal Institute of Technology, Brinellv\u00e4gen 83, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0000-0001-9556-6856","affiliations":[{"raw_affiliation_string":"Department of Machine Design, KTH Royal Institute of Technology, Brinellv\u00e4gen 83, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054955661","display_name":"Lei Feng","orcid":"https://orcid.org/0000-0001-5703-5923"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Lei Feng","raw_affiliation_strings":["Department of Machine Design, KTH Royal Institute of Technology, Brinellv\u00e4gen 83, Stockholm, Sweden"],"raw_orcid":"https://orcid.org/0000-0001-5703-5923","affiliations":[{"raw_affiliation_string":"Department of Machine Design, KTH Royal Institute of Technology, Brinellv\u00e4gen 83, Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049675914","display_name":"Wenyao Zhu","orcid":"https://orcid.org/0000-0002-4911-0257"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Wenyao Zhu","raw_affiliation_strings":["Division of Electronics and Embedded Systems, KTH Royal Institute of Technology, Electrum 229, Kista, Sweden"],"raw_orcid":"https://orcid.org/0000-0002-4911-0257","affiliations":[{"raw_affiliation_string":"Division of Electronics and Embedded Systems, KTH Royal Institute of Technology, Electrum 229, Kista, Sweden","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100392629"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":null,"apc_paid":{"value":1671,"currency":"EUR","value_usd":1802},"fwci":1.4875,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.8142343,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"70","issue":"6","first_page":"5551","last_page":"5564"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10808","display_name":"Electric and Hybrid Vehicle Technologies","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/T10808","display_name":"Electric and Hybrid Vehicle Technologies","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/T10768","display_name":"Electric Vehicles and Infrastructure","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10663","display_name":"Advanced Battery Technologies Research","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2203","display_name":"Automotive 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/optimal-control","display_name":"Optimal control","score":0.5550158023834229},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.542610764503479},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5358840823173523},{"id":"https://openalex.org/keywords/fuel-efficiency","display_name":"Fuel efficiency","score":0.5047229528427124},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.45310115814208984},{"id":"https://openalex.org/keywords/torque","display_name":"Torque","score":0.44915643334388733},{"id":"https://openalex.org/keywords/automotive-engineering","display_name":"Automotive engineering","score":0.44428926706314087},{"id":"https://openalex.org/keywords/electric-vehicle","display_name":"Electric vehicle","score":0.43080225586891174},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.428529292345047},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.41734105348587036},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.33749157190322876},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3275930881500244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2266940176486969},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19090968370437622},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.10534599423408508}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5550158023834229},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.542610764503479},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5358840823173523},{"id":"https://openalex.org/C45882903","wikidata":"https://www.wikidata.org/wiki/Q5042317","display_name":"Fuel efficiency","level":2,"score":0.5047229528427124},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.45310115814208984},{"id":"https://openalex.org/C144171764","wikidata":"https://www.wikidata.org/wiki/Q48103","display_name":"Torque","level":2,"score":0.44915643334388733},{"id":"https://openalex.org/C171146098","wikidata":"https://www.wikidata.org/wiki/Q124192","display_name":"Automotive engineering","level":1,"score":0.44428926706314087},{"id":"https://openalex.org/C2776422217","wikidata":"https://www.wikidata.org/wiki/Q13629441","display_name":"Electric vehicle","level":3,"score":0.43080225586891174},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.428529292345047},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.41734105348587036},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.33749157190322876},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3275930881500244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2266940176486969},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19090968370437622},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.10534599423408508},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tvt.2021.3075729","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tvt.2021.3075729","pdf_url":"https://ieeexplore.ieee.org/ielx7/25/9477511/09416826.pdf","source":{"id":"https://openalex.org/S10936095","display_name":"IEEE Transactions on Vehicular Technology","issn_l":"0018-9545","issn":["0018-9545","1939-9359"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Vehicular Technology","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1109/tvt.2021.3075729","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tvt.2021.3075729","pdf_url":"https://ieeexplore.ieee.org/ielx7/25/9477511/09416826.pdf","source":{"id":"https://openalex.org/S10936095","display_name":"IEEE Transactions on Vehicular Technology","issn_l":"0018-9545","issn":["0018-9545","1939-9359"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Vehicular Technology","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.8799999952316284,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320322509","display_name":"Kungliga Tekniska H\u00f6gskolan","ror":"https://ror.org/026vcq606"},{"id":"https://openalex.org/F4320322725","display_name":"China Scholarship Council","ror":"https://ror.org/04atp4p48"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3177642153.pdf","grobid_xml":"https://content.openalex.org/works/W3177642153.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W650973245","https://openalex.org/W2004262618","https://openalex.org/W2017749620","https://openalex.org/W2025183193","https://openalex.org/W2027407116","https://openalex.org/W2041319171","https://openalex.org/W2047111123","https://openalex.org/W2070589866","https://openalex.org/W2074558487","https://openalex.org/W2087149600","https://openalex.org/W2095379320","https://openalex.org/W2099360030","https://openalex.org/W2106868107","https://openalex.org/W2110884433","https://openalex.org/W2117326974","https://openalex.org/W2123953888","https://openalex.org/W2124085945","https://openalex.org/W2165579389","https://openalex.org/W2190859449","https://openalex.org/W2220460425","https://openalex.org/W2232021528","https://openalex.org/W2236204240","https://openalex.org/W2287936343","https://openalex.org/W2330761921","https://openalex.org/W2466636338","https://openalex.org/W2479780626","https://openalex.org/W2501655773","https://openalex.org/W2528691896","https://openalex.org/W2567832009","https://openalex.org/W2591714971","https://openalex.org/W2728105440","https://openalex.org/W2885610882","https://openalex.org/W2886578595","https://openalex.org/W2898483287","https://openalex.org/W2904025397","https://openalex.org/W2904086465","https://openalex.org/W2922137599","https://openalex.org/W2989832664","https://openalex.org/W2990975667","https://openalex.org/W2991322542","https://openalex.org/W2996110925","https://openalex.org/W4300825532"],"related_works":["https://openalex.org/W4285537323","https://openalex.org/W1932159282","https://openalex.org/W2379312070","https://openalex.org/W2136173754","https://openalex.org/W2332086753","https://openalex.org/W2110050003","https://openalex.org/W2613864214","https://openalex.org/W2953025626","https://openalex.org/W2499081552","https://openalex.org/W1988590764"],"abstract_inverted_index":{"This":[0],"paper":[1],"improves":[2],"the":[3,31,40,46,67,92,100,103,108,114,123,138,141,154,163,182,196,215],"fuel":[4,148,179,212],"efficiency":[5,23,149,180,213],"of":[6,69,153,162,195],"a":[7,35,83],"student-made":[8],"parallel":[9],"hybrid":[10],"electric":[11,115],"racing":[12],"car":[13,53],"whose":[14],"internal":[15],"combustion":[16],"engine":[17],"(ICE)":[18],"either":[19],"operates":[20],"with":[21,218],"peak":[22],"or":[24],"is":[25,78,87,97,199],"turned":[26],"off.":[27],"The":[28,119,132,147,174,193],"control":[29],"to":[30,39,80,90,106],"ICE":[32,110,217],"thus":[33],"becomes":[34],"binary":[36,216],"problem.":[37],"Owing":[38],"very":[41],"limited":[42],"computation":[43],"resource":[44],"onboard,":[45],"energy":[47],"management":[48],"strategy":[49],"(EMS)":[50],"for":[51,102,214],"this":[52],"must":[54],"have":[55],"small":[56],"time":[57],"and":[58,73,113,150,170,203],"space":[59],"complexities.":[60],"A":[61],"computationally":[62],"efficient":[63],"controller":[64,156,198],"that":[65],"combines":[66],"advantages":[68],"dynamic":[70],"programming":[71],"(DP)":[72],"Pontryagin's":[74],"minimum":[75],"principle":[76],"(PMP)":[77],"developed":[79],"run":[81],"on":[82],"low-cost":[84],"microprocessor.":[85],"DP":[86],"employed":[88],"offline":[89],"calculate":[91],"optimal":[93,124],"speed":[94],"trajectory,":[95],"which":[96],"used":[98],"as":[99,181],"reference":[101],"online":[104],"PMP":[105,121],"determine":[107],"real-time":[109],"on/off":[111],"status":[112],"motor":[116],"(EM)":[117],"torques.":[118],"normal":[120],"derives":[122],"costate":[125,139],"trajectory":[126],"through":[127,166],"solving":[128],"partial":[129],"differential":[130],"equations.":[131],"proposed":[133,155],"quasi-PMP":[134],"(Q-PMP)":[135],"method":[136,176],"finds":[137],"from":[140],"value":[142],"function":[143],"obtained":[144],"by":[145],"DP.":[146],"computational":[151],"complexity":[152],"are":[157],"compared":[158,200],"against":[159],"several":[160],"state":[161],"art":[164],"methods":[165],"both":[167],"model-in-the-loop":[168],"(MIL)":[169],"processor-in-the-loop":[171],"(PIL)":[172],"simulations.":[173],"new":[175],"reaches":[177],"similar":[178],"explicit":[183],"DP,":[184],"but":[185],"requires":[186],"less":[187],"than":[188],"1%":[189],"onboard":[190],"flash":[191],"memory.":[192],"performance":[194],"Q-PMP":[197],"between":[201],"binary-controlled":[202],"continuously":[204],"controlled":[205],"ICEs.":[206],"It":[207],"achieves":[208],"roughly":[209],"12%":[210],"higher":[211],"only":[219],"approximately":[220],"1/3":[221],"CPU":[222],"utilization.":[223]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":1}],"updated_date":"2026-05-16T08:24:45.110214","created_date":"2025-10-10T00:00:00"}
