{"id":"https://openalex.org/W7127613245","doi":"https://doi.org/10.1109/tvt.2026.3661076","title":"Optimal Cluster Formation Control for Air-Sea Heterogeneous Multi-Robot Systems: A Predefined-Time Estimator-Based Reinforcement Learning Approach","display_name":"Optimal Cluster Formation Control for Air-Sea Heterogeneous Multi-Robot Systems: A Predefined-Time Estimator-Based Reinforcement Learning Approach","publication_year":2026,"publication_date":"2026-02-04","ids":{"openalex":"https://openalex.org/W7127613245","doi":"https://doi.org/10.1109/tvt.2026.3661076"},"language":null,"primary_location":{"id":"doi:10.1109/tvt.2026.3661076","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2026.3661076","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101728170","display_name":"Caixia Chen","orcid":"https://orcid.org/0000-0002-6928-6188"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Caixia Chen","raw_affiliation_strings":["School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China"],"raw_orcid":"https://orcid.org/0009-0006-6594-7862","affiliations":[{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124989315","display_name":"Hengyu Li","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hengyu Li","raw_affiliation_strings":["School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-2243-5908","affiliations":[{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124986682","display_name":"Jingyi Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I4210127530","display_name":"Jining University","ror":"https://ror.org/037rvh518","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210127530"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jingyi Liu","raw_affiliation_strings":["School of Mathematics and Big Data, Jining University, Qufu, China","School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0001-6251-6051","affiliations":[{"raw_affiliation_string":"School of Mathematics and Big Data, Jining University, Qufu, China","institution_ids":["https://openalex.org/I4210127530"]},{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124973203","display_name":"Jun Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]},{"id":"https://openalex.org/I4210127530","display_name":"Jining University","ror":"https://ror.org/037rvh518","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210127530"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jun Liu","raw_affiliation_strings":["School of Mathematics and Big Data, Jining University, Qufu, China","School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-2154-4037","affiliations":[{"raw_affiliation_string":"School of Mathematics and Big Data, Jining University, Qufu, China","institution_ids":["https://openalex.org/I4210127530"]},{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124995997","display_name":"Chen Peng","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen Peng","raw_affiliation_strings":["School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0003-1232-6959","affiliations":[{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5125043710","display_name":"Shaorong Xie","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shaorong Xie","raw_affiliation_strings":["School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-8016-9310","affiliations":[{"raw_affiliation_string":"School of Mechatronic Engineering and Automation, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10600201,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"75","issue":"7","first_page":"12440","last_page":"12452"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.7185999751091003,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.7185999751091003,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.21130000054836273,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.01269999984651804,"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/reinforcement-learning","display_name":"Reinforcement learning","score":0.644599974155426},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.599399983882904},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5672000050544739},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5601999759674072},{"id":"https://openalex.org/keywords/cluster","display_name":"Cluster (spacecraft)","score":0.4657000005245209},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.39730000495910645},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.3930000066757202},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.38370001316070557},{"id":"https://openalex.org/keywords/vehicle-dynamics","display_name":"Vehicle dynamics","score":0.38029998540878296}],"concepts":[{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.644599974155426},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.599399983882904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.58160001039505},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5672000050544739},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5601999759674072},{"id":"https://openalex.org/C164866538","wikidata":"https://www.wikidata.org/wiki/Q367351","display_name":"Cluster (spacecraft)","level":2,"score":0.4657000005245209},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.39730000495910645},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.3930000066757202},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.38370001316070557},{"id":"https://openalex.org/C79487989","wikidata":"https://www.wikidata.org/wiki/Q934680","display_name":"Vehicle dynamics","level":2,"score":0.38029998540878296},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.37459999322891235},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.37400001287460327},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3720000088214874},{"id":"https://openalex.org/C36662352","wikidata":"https://www.wikidata.org/wiki/Q6008560","display_name":"Sliding mode control","level":3,"score":0.37070000171661377},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.35420000553131104},{"id":"https://openalex.org/C124527596","wikidata":"https://www.wikidata.org/wiki/Q17029359","display_name":"Hierarchical control system","level":3,"score":0.3521000146865845},{"id":"https://openalex.org/C96442724","wikidata":"https://www.wikidata.org/wiki/Q242188","display_name":"Invertible matrix","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C2775936607","wikidata":"https://www.wikidata.org/wiki/Q466845","display_name":"Tracking (education)","level":2,"score":0.3301999866962433},{"id":"https://openalex.org/C2776829284","wikidata":"https://www.wikidata.org/wiki/Q1341651","display_name":"Lyapunov stability","level":3,"score":0.3077999949455261},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.2955000102519989},{"id":"https://openalex.org/C90509273","wikidata":"https://www.wikidata.org/wiki/Q11012","display_name":"Robot","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C19966478","wikidata":"https://www.wikidata.org/wiki/Q4810574","display_name":"Mobile robot","level":3,"score":0.27570000290870667},{"id":"https://openalex.org/C77405623","wikidata":"https://www.wikidata.org/wiki/Q598451","display_name":"System dynamics","level":2,"score":0.27090001106262207},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2558000087738037},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.25189998745918274}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tvt.2026.3661076","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvt.2026.3661076","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Vehicular Technology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.8057675957679749}],"awards":[{"id":"https://openalex.org/G1514543780","display_name":null,"funder_award_id":"2024M751933","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G2029980506","display_name":null,"funder_award_id":"62073209","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2802250152","display_name":null,"funder_award_id":"62421004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5602108062","display_name":null,"funder_award_id":"62403298","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/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"investigates":[2],"the":[3,35,82,95,103,116,134,154,168,188,191],"problem":[4,36],"of":[5,84,133,156,190],"optimal":[6,50,130,149],"cluster":[7,144],"formation":[8,43,97,145,160],"control":[9,29,117,123,132],"for":[10],"air\u2013sea":[11,170],"heterogeneous":[12,135],"multi-robot":[13],"systems":[14],"(HMRSs)":[15],"subject":[16],"to":[17,114,127,186],"external":[18],"disturbances":[19],"and":[20,45,181],"energy":[21],"constraints.":[22],"To":[23],"address":[24],"this":[25],"challenge,":[26],"a":[27,54,90,106],"hierarchical":[28,139],"framework":[30,111,140],"is":[31,62,112],"proposed,":[32],"which":[33,64],"decomposes":[34],"into":[37],"two":[38],"sub-tasks:":[39],"distributed":[40,55],"sliding-mode-based":[41],"predefined-time":[42,57,143],"estimation":[44,60,146],"reinforcement":[46],"learning":[47],"(RL)-based":[48],"local":[49,129,148],"tracking":[51,131,150],"control.":[52,161],"First,":[53],"nonsingular":[56],"sliding":[58],"mode":[59],"algorithm":[61],"designed,":[63],"not":[65],"only":[66],"effectively":[67,141],"eliminates":[68],"system":[69],"dimensional":[70],"heterogeneity":[71],"but":[72],"also":[73],"ensures":[74],"that":[75],"each":[76],"follower":[77],"robot":[78],"can":[79],"accurately":[80],"estimate":[81],"state":[83],"its":[85],"corresponding":[86],"virtual":[87],"leader":[88],"within":[89],"predefined":[91],"time,":[92],"thereby":[93],"generating":[94],"desired":[96],"con":[98],"figuration.":[99],"Subsequently,":[100],"based":[101],"on":[102],"estimated":[104],"information,":[105],"neural":[107],"network-driven":[108],"critic\u2013actor":[109],"RL":[110,158],"constructed":[113],"optimize":[115],"inputs.":[118],"By":[119],"incorporating":[120],"backstepping,":[121],"intermediate":[122],"signals":[124],"are":[125,184],"designed":[126],"achieve":[128],"system.":[136],"The":[137],"proposed":[138,192],"decouples":[142],"from":[147],"control,":[151],"significantly":[152],"reducing":[153],"complexity":[155],"applying":[157],"in":[159],"Moreover,":[162],"compared":[163],"with":[164],"existing":[165],"simplified":[166],"models,":[167],"established":[169],"HMRS":[171],"model":[172],"achieves":[173],"higher":[174],"accuracy.":[175],"Finally,":[176],"rigorous":[177],"Lyapunov":[178],"stability":[179],"analysis":[180],"numerical":[182],"simulations":[183],"conducted":[185],"verify":[187],"effectiveness":[189],"algorithm.":[193]},"counts_by_year":[],"updated_date":"2026-07-21T05:50:15.549392","created_date":"2026-02-06T00:00:00"}