{"id":"https://openalex.org/W2946973591","doi":"https://doi.org/10.1109/access.2019.2919249","title":"Optimized Backstepping Design for Ship Course Following Control Based on Actor-Critic Architecture With Input Saturation","display_name":"Optimized Backstepping Design for Ship Course Following Control Based on Actor-Critic Architecture With Input Saturation","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2946973591","doi":"https://doi.org/10.1109/access.2019.2919249","mag":"2946973591"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2919249","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2919249","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08723321.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08723321.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015996724","display_name":"Yuming Bai","orcid":null},"institutions":[{"id":"https://openalex.org/I43313876","display_name":"Dalian Maritime University","ror":"https://ror.org/002b7nr53","country_code":"CN","type":"education","lineage":["https://openalex.org/I43313876"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuming Bai","raw_affiliation_strings":["Navigation College, Dalian Maritime University, Dalian, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Navigation College, Dalian Maritime University, Dalian, China","institution_ids":["https://openalex.org/I43313876"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064123400","display_name":"Yuchi Cao","orcid":"https://orcid.org/0000-0001-6486-5677"},"institutions":[{"id":"https://openalex.org/I43313876","display_name":"Dalian Maritime University","ror":"https://ror.org/002b7nr53","country_code":"CN","type":"education","lineage":["https://openalex.org/I43313876"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuchi Cao","raw_affiliation_strings":["Navigation College, Dalian Maritime University, Dalian, China"],"raw_orcid":"https://orcid.org/0000-0001-6486-5677","affiliations":[{"raw_affiliation_string":"Navigation College, Dalian Maritime University, Dalian, China","institution_ids":["https://openalex.org/I43313876"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025349097","display_name":"Tieshan Li","orcid":"https://orcid.org/0000-0003-0474-953X"},"institutions":[{"id":"https://openalex.org/I43313876","display_name":"Dalian Maritime University","ror":"https://ror.org/002b7nr53","country_code":"CN","type":"education","lineage":["https://openalex.org/I43313876"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tieshan Li","raw_affiliation_strings":["Navigation College, Dalian Maritime University, Dalian, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Navigation College, Dalian Maritime University, Dalian, China","institution_ids":["https://openalex.org/I43313876"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I43313876"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":2.135,"has_fulltext":true,"cited_by_count":20,"citation_normalized_percentile":{"value":0.87461533,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"7","issue":null,"first_page":"73516","last_page":"73528"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9998999834060669,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9998999834060669,"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.9995999932289124,"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/T11192","display_name":"Underwater Vehicles and Communication Systems","score":0.9922999739646912,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/backstepping","display_name":"Backstepping","score":0.9344805479049683},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6792514324188232},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.67902010679245},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.6425413489341736},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.6102232933044434},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.517818033695221},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5162451267242432},{"id":"https://openalex.org/keywords/tracking-error","display_name":"Tracking error","score":0.49718692898750305},{"id":"https://openalex.org/keywords/control-engineering","display_name":"Control engineering","score":0.4586179256439209},{"id":"https://openalex.org/keywords/lyapunov-stability","display_name":"Lyapunov stability","score":0.4497803747653961},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.3582664728164673},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.3564009666442871},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2926177978515625},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.28675949573516846},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.24686956405639648},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.23023030161857605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.16707435250282288},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.154165118932724}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.9344805479049683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6792514324188232},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.67902010679245},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.6425413489341736},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.6102232933044434},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.517818033695221},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5162451267242432},{"id":"https://openalex.org/C183356978","wikidata":"https://www.wikidata.org/wiki/Q1779213","display_name":"Tracking error","level":3,"score":0.49718692898750305},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.4586179256439209},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.4497803747653961},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.3582664728164673},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.3564009666442871},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2926177978515625},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.28675949573516846},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.24686956405639648},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.23023030161857605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.16707435250282288},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.154165118932724},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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":2,"locations":[{"id":"doi:10.1109/access.2019.2919249","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2919249","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08723321.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b362bb97886a47158fc7434d15060fb1","is_oa":true,"landing_page_url":"https://doaj.org/article/b362bb97886a47158fc7434d15060fb1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 7, Pp 73516-73528 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2919249","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2919249","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08723321.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8799999952316284,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1340777148","display_name":null,"funder_award_id":"2018J11CY022","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G1759699137","display_name":null,"funder_award_id":"61803064","funder_id":"https://openalex.org/F4320323086","funder_display_name":"Natural Science Foundation of Liaoning Province"},{"id":"https://openalex.org/G2205113730","display_name":"\u591a\u6e90\u5e72\u6270\u4e0b\u5177\u6709\u901a\u8baf\u7f51\u7edc\u62d3\u6251\u91cd\u6784\u673a\u5236\u7684\u591a\u667a\u80fd\u4f53\u7cfb\u7edf\u5305\u542b\u63a7\u5236\u53ca\u5e94\u7528","funder_award_id":"61803064","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3131769378","display_name":null,"funder_award_id":"2018J11CY022","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3638983309","display_name":null,"funder_award_id":"61803064","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6155485761","display_name":null,"funder_award_id":"61751202","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G653700208","display_name":null,"funder_award_id":"61751202","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6742440219","display_name":null,"funder_award_id":"61751202","funder_id":"https://openalex.org/F4320323086","funder_display_name":"Natural Science Foundation of Liaoning Province"},{"id":"https://openalex.org/G694192086","display_name":null,"funder_award_id":"3132019126","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6977279421","display_name":null,"funder_award_id":"20170540093","funder_id":"https://openalex.org/F4320323086","funder_display_name":"Natural Science Foundation of Liaoning Province"},{"id":"https://openalex.org/G7611596349","display_name":null,"funder_award_id":"61751205","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7847989482","display_name":null,"funder_award_id":"2018J11CY022","funder_id":"https://openalex.org/F4320323086","funder_display_name":"Natural Science Foundation of Liaoning Province"},{"id":"https://openalex.org/G827077099","display_name":null,"funder_award_id":"3132019124","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G936074557","display_name":null,"funder_award_id":"61572540","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323086","display_name":"Natural Science Foundation of Liaoning Province","ror":null},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2946973591.pdf","grobid_xml":"https://content.openalex.org/works/W2946973591.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1966556797","https://openalex.org/W1988876996","https://openalex.org/W1989403823","https://openalex.org/W2002011878","https://openalex.org/W2008072208","https://openalex.org/W2042814461","https://openalex.org/W2042866592","https://openalex.org/W2043838118","https://openalex.org/W2049933349","https://openalex.org/W2065905935","https://openalex.org/W2072773743","https://openalex.org/W2089904313","https://openalex.org/W2101602531","https://openalex.org/W2113442785","https://openalex.org/W2121570671","https://openalex.org/W2124659043","https://openalex.org/W2124776405","https://openalex.org/W2133869087","https://openalex.org/W2134024695","https://openalex.org/W2262108890","https://openalex.org/W2306110109","https://openalex.org/W2489526136","https://openalex.org/W2597796803","https://openalex.org/W2727086434","https://openalex.org/W2729186515","https://openalex.org/W2741071150","https://openalex.org/W2751024589","https://openalex.org/W2775542401","https://openalex.org/W2777246076","https://openalex.org/W2811002385","https://openalex.org/W2887519063","https://openalex.org/W2897009016","https://openalex.org/W2900974632","https://openalex.org/W2906822486","https://openalex.org/W2906995901","https://openalex.org/W2907917818","https://openalex.org/W2910023039"],"related_works":["https://openalex.org/W2032834442","https://openalex.org/W3153900688","https://openalex.org/W2115544975","https://openalex.org/W2902017027","https://openalex.org/W1654696814","https://openalex.org/W4291598237","https://openalex.org/W2766998270","https://openalex.org/W4292330635","https://openalex.org/W3168988147","https://openalex.org/W4239477580"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3],"course":[4,29,138],"following":[5,139],"control":[6,24,79,145],"method":[7],"for":[8,75],"ships":[9],"based":[10],"on":[11,39,137],"optimized":[12],"backstepping":[13,17],"(OB)":[14],"technology.":[15],"The":[16,70,109],"technology":[18],"is":[19,56],"employed":[20,100],"as":[21],"the":[22,27,34,40,51,60,64,78,82,88,103,112,132,144],"main":[23],"framework":[25],"since":[26],"ship":[28],"can":[30,115],"be":[31,116],"modeled":[32],"in":[33,62,148],"strict":[35],"feedback":[36],"form.":[37],"Based":[38],"actor-critic":[41],"architecture":[42],"and":[43,95,124,130,135,140],"radial":[44],"basis":[45],"function":[46,98],"(RBF)":[47],"neural":[48],"network":[49],"(NN),":[50],"reinforcement":[52],"learning":[53],"(RL)":[54],"strategy":[55],"introduced":[57],"to":[58,101,128],"avoid":[59],"difficulty":[61],"solving":[63],"traditional":[65],"Hamilton-Jacobi-Bellman":[66],"(HJB)":[67],"equation":[68],"directly.":[69],"actor":[71],"NNs":[72,84],"are":[73,99,126],"used":[74],"carrying":[76],"out":[77],"law,":[80],"while":[81],"critic":[83],"aim":[85],"at":[86],"evaluating":[87],"tracking":[89],"performance.":[90],"An":[91],"auxiliary":[92],"design":[93],"system":[94,114],"Gaussian":[96],"error":[97],"handle":[102],"practical":[104],"problem":[105],"of":[106,111,143],"input":[107],"saturation.":[108],"stability":[110],"closed-loop":[113],"guaranteed":[117],"via":[118],"Lyapunov":[119],"theory.":[120],"Finally,":[121],"simulation":[122],"examples":[123],"comparison":[125],"provided":[127],"demonstrate":[129],"verify":[131],"superior":[133],"performance":[134],"advantages":[136],"energy":[141],"saving":[142],"scheme":[146],"proposed":[147],"this":[149],"paper.":[150]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}