{"id":"https://openalex.org/W7121167581","doi":"https://doi.org/10.1093/imamci/dnaf046","title":"Extremum seeking boundary control for PDE systems using PINNs","display_name":"Extremum seeking boundary control for PDE systems using PINNs","publication_year":2025,"publication_date":"2025-12-12","ids":{"openalex":"https://openalex.org/W7121167581","doi":"https://doi.org/10.1093/imamci/dnaf046"},"language":"en","primary_location":{"id":"doi:10.1093/imamci/dnaf046","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnaf046","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","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/A5103680071","display_name":"Hang Guo","orcid":"https://orcid.org/0009-0003-0464-3572"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haojin Guo","raw_affiliation_strings":["Institute of Precision Guidance and Control, School of Astronautics, Northwestern Polytechnical University , Xi\u2019an 710072, Shaanxi ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Precision Guidance and Control, School of Astronautics, Northwestern Polytechnical University , Xi\u2019an 710072, Shaanxi ,","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101861274","display_name":"Zongyi Guo","orcid":"https://orcid.org/0000-0001-6837-9924"},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zongyi Guo","raw_affiliation_strings":["Institute of Precision Guidance and Control, School of Astronautics, Northwestern Polytechnical University , Xi\u2019an 710072, Shaanxi ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Precision Guidance and Control, School of Astronautics, Northwestern Polytechnical University , Xi\u2019an 710072, Shaanxi ,","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065916798","display_name":"Jianguo GUO","orcid":null},"institutions":[{"id":"https://openalex.org/I17145004","display_name":"Northwestern Polytechnical University","ror":"https://ror.org/01y0j0j86","country_code":"CN","type":"education","lineage":["https://openalex.org/I17145004"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jianguo Guo","raw_affiliation_strings":["Institute of Precision Guidance and Control, School of Astronautics, Northwestern Polytechnical University , Xi\u2019an 710072, Shaanxi ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Precision Guidance and Control, School of Astronautics, Northwestern Polytechnical University , Xi\u2019an 710072, Shaanxi ,","institution_ids":["https://openalex.org/I17145004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087451137","display_name":"Tiago Roux Oliveira","orcid":"https://orcid.org/0000-0002-2232-8715"},"institutions":[{"id":"https://openalex.org/I40034438","display_name":"Universidade do Estado do Rio de Janeiro","ror":"https://ror.org/0198v2949","country_code":"BR","type":"education","lineage":["https://openalex.org/I40034438"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Tiago Roux Oliveira","raw_affiliation_strings":["Department of Electronics and Telecommunication Engineering, State University of Rio de Janeiro , Rio de Janeiro, RJ 20550-900 \u00a0"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Telecommunication Engineering, State University of Rio de Janeiro , Rio de Janeiro, RJ 20550-900 \u00a0","institution_ids":["https://openalex.org/I40034438"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101861274"],"corresponding_institution_ids":["https://openalex.org/I17145004"],"apc_list":{"value":2582,"currency":"GBP","value_usd":3167},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.58006957,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14083","display_name":"Extremum Seeking Control Systems","score":0.9302999973297119,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.9302999973297119,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.02250000089406967,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12794","display_name":"Adaptive Dynamic Programming Control","score":0.018799999728798866,"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/embedding","display_name":"Embedding","score":0.6456999778747559},{"id":"https://openalex.org/keywords/cascade","display_name":"Cascade","score":0.608299970626831},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5910000205039978},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.583299994468689},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5615000128746033},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5552999973297119},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5328999757766724},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5012999773025513},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.3743000030517578},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.37279999256134033}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.6456999778747559},{"id":"https://openalex.org/C34146451","wikidata":"https://www.wikidata.org/wiki/Q5048094","display_name":"Cascade","level":2,"score":0.608299970626831},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5910000205039978},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.583299994468689},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5615000128746033},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5552999973297119},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5328999757766724},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5113000273704529},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5012999773025513},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.40860000252723694},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3743000030517578},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.37279999256134033},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3431999981403351},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33739998936653137},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.3305000066757202},{"id":"https://openalex.org/C81074085","wikidata":"https://www.wikidata.org/wiki/Q366872","display_name":"Motion planning","level":3,"score":0.3165999948978424},{"id":"https://openalex.org/C155032097","wikidata":"https://www.wikidata.org/wiki/Q798503","display_name":"Backpropagation","level":3,"score":0.3124000132083893},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.31150001287460327},{"id":"https://openalex.org/C47822265","wikidata":"https://www.wikidata.org/wiki/Q854457","display_name":"Complex system","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.299699991941452},{"id":"https://openalex.org/C3018651601","wikidata":"https://www.wikidata.org/wiki/Q183635","display_name":"Feedback control","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.28349998593330383},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.28220000863075256},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C104267543","wikidata":"https://www.wikidata.org/wiki/Q208163","display_name":"Signal processing","level":3,"score":0.2784999907016754},{"id":"https://openalex.org/C145565327","wikidata":"https://www.wikidata.org/wiki/Q852514","display_name":"Motion control","level":3,"score":0.27709999680519104},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.2752000093460083},{"id":"https://openalex.org/C116672817","wikidata":"https://www.wikidata.org/wiki/Q1454986","display_name":"Physical system","level":2,"score":0.26989999413490295},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.25679999589920044},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.2522999942302704}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1093/imamci/dnaf046","is_oa":false,"landing_page_url":"https://doi.org/10.1093/imamci/dnaf046","pdf_url":null,"source":{"id":"https://openalex.org/S162756791","display_name":"IMA Journal of Mathematical Control and Information","issn_l":"0265-0754","issn":["0265-0754","1471-6887"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311648","host_organization_name":"Oxford University Press","host_organization_lineage":["https://openalex.org/P4310311648","https://openalex.org/P4310311647"],"host_organization_lineage_names":["Oxford University Press","University of Oxford"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IMA Journal of Mathematical Control and Information","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.46355560421943665,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G4701702971","display_name":null,"funder_award_id":"92271109","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G958898749","display_name":null,"funder_award_id":"52272404","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/F4320321091","display_name":"Coordena\u00e7\u00e3o de Aperfei\u00e7oamento de Pessoal de N\u00edvel Superior","ror":"https://ror.org/00x0ma614"},{"id":"https://openalex.org/F4320322025","display_name":"Conselho Nacional de Desenvolvimento Cient\u00edfico e Tecnol\u00f3gico","ror":"https://ror.org/03swz6y49"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W564609686","https://openalex.org/W1978871245","https://openalex.org/W1982852315","https://openalex.org/W1989593999","https://openalex.org/W2019174039","https://openalex.org/W2025496609","https://openalex.org/W2028811441","https://openalex.org/W2031532646","https://openalex.org/W2046439822","https://openalex.org/W2095062552","https://openalex.org/W2147574995","https://openalex.org/W2407938586","https://openalex.org/W2499641798","https://openalex.org/W2767665404","https://openalex.org/W2810641590","https://openalex.org/W2888949633","https://openalex.org/W2899283552","https://openalex.org/W2924767380","https://openalex.org/W2974916071","https://openalex.org/W3000182140","https://openalex.org/W3000699637","https://openalex.org/W3022058968","https://openalex.org/W3037232681","https://openalex.org/W3048051055","https://openalex.org/W3091275821","https://openalex.org/W3176244639","https://openalex.org/W3190288780","https://openalex.org/W4205222570","https://openalex.org/W4226030552","https://openalex.org/W4288039037","https://openalex.org/W4313135766","https://openalex.org/W4368352854","https://openalex.org/W4377819143","https://openalex.org/W4385973818","https://openalex.org/W4388339706","https://openalex.org/W4390120059","https://openalex.org/W4390224269","https://openalex.org/W4391046545","https://openalex.org/W4393349650","https://openalex.org/W4403389162","https://openalex.org/W4404625186","https://openalex.org/W4407128403","https://openalex.org/W4407949421","https://openalex.org/W4408285785","https://openalex.org/W4409696351","https://openalex.org/W4410076591"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"Extremum":[1],"seeking":[2],"(ES)":[3],"is":[4,81],"an":[5],"effective":[6],"real-time":[7],"optimization":[8],"method":[9],"for":[10,69,85,103,124,132],"partial":[11],"differential":[12],"equation":[13],"(PDE)":[14],"systems":[15,70,127],"in":[16,25,94],"cascade":[17],"with":[18],"non-linear":[19,105],"quadratic":[20],"maps.":[21],"To":[22],"address":[23],"PDEs":[24,87],"the":[26,37,95,120,130,144],"feedback":[27],"loop,":[28],"a":[29,34,82,112],"boundary":[30],"control":[31],"law":[32],"and":[33,74,106,117,128],"re-design":[35],"of":[36],"additive":[38],"probing":[39],"signal":[40],"are":[41],"mandatory.":[42],"The":[43,136],"latter,":[44],"commonly":[45],"called":[46],"\u2018trajectory":[47],"generation\u2019":[48],"or":[49],"\u2018motion":[50],"planning\u2019,":[51],"involves":[52],"designing":[53],"perturbation":[54,141],"signals":[55],"that":[56],"anticipate":[57],"their":[58],"propagation":[59],"through":[60],"PDEs.":[61,76],"Specifically,":[62],"this":[63],"requires":[64],"solving":[65,86],"motion":[66,121],"planning":[67,122],"problems":[68],"governed":[71],"by":[72,88],"parabolic":[73],"hyperbolic":[75],"Physics-informed":[77],"neural":[78,96],"networks":[79],"(PINNs)":[80],"powerful":[83],"tool":[84],"embedding":[89],"physical":[90],"laws":[91],"as":[92],"constraints":[93],"network\u2019s":[97],"loss":[98],"function,":[99],"enabling":[100],"efficient":[101],"solutions":[102],"high-dimensional,":[104],"complex":[107],"problems.":[108],"This":[109],"paper":[110],"proposes":[111],"novel":[113],"construction":[114],"integrating":[115],"PINN":[116],"ES,":[118],"automating":[119],"process":[123],"specific":[125],"PDE":[126,145],"eliminating":[129],"need":[131],"case-by-case":[133],"analytical":[134],"derivations.":[135],"proposed":[137],"strategy":[138],"efficiently":[139],"extracts":[140],"signals,":[142],"optimizing":[143],"system.":[146]},"counts_by_year":[],"updated_date":"2026-06-18T08:10:14.011955","created_date":"2026-01-11T00:00:00"}