{"id":"https://openalex.org/W4408285443","doi":"https://doi.org/10.1109/tac.2025.3550074","title":"Stabilization of a Class of Large-Scale Systems of Linear Hyperbolic PDEs via Continuum Approximation of Exact Backstepping Kernels","display_name":"Stabilization of a Class of Large-Scale Systems of Linear Hyperbolic PDEs via Continuum Approximation of Exact Backstepping Kernels","publication_year":2025,"publication_date":"2025-03-10","ids":{"openalex":"https://openalex.org/W4408285443","doi":"https://doi.org/10.1109/tac.2025.3550074"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3550074","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2025.3550074","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1109/tac.2025.3550074","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5006418694","display_name":"Jukka-Pekka Humaloja","orcid":"https://orcid.org/0000-0002-6926-8756"},"institutions":[{"id":"https://openalex.org/I55741626","display_name":"Technical University of Crete","ror":"https://ror.org/03f8bz564","country_code":"GR","type":"education","lineage":["https://openalex.org/I55741626"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Jukka-Pekka Humaloja","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece","institution_ids":["https://openalex.org/I55741626"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020100534","display_name":"Nikolaos Bekiaris\u2010Liberis","orcid":"https://orcid.org/0000-0002-4223-2681"},"institutions":[{"id":"https://openalex.org/I55741626","display_name":"Technical University of Crete","ror":"https://ror.org/03f8bz564","country_code":"GR","type":"education","lineage":["https://openalex.org/I55741626"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Nikolaos Bekiaris-Liberis","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Technical University of Crete, Chania, Greece","institution_ids":["https://openalex.org/I55741626"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5006418694"],"corresponding_institution_ids":["https://openalex.org/I55741626"],"apc_list":null,"apc_paid":null,"fwci":4.6468,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.94085129,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":98},"biblio":{"volume":"70","issue":"9","first_page":"5957","last_page":"5972"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9860000014305115,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9860000014305115,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9294000267982483,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9139999747276306,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.8935493230819702},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6036315560340881},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.571821928024292},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5492671132087708},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.47522929310798645},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.46676915884017944},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4570380449295044},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.41267579793930054},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3831775486469269},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3284558355808258},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25158682465553284},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19764280319213867},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.08875918388366699},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.05482819676399231}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.8935493230819702},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6036315560340881},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.571821928024292},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5492671132087708},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.47522929310798645},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.46676915884017944},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4570380449295044},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.41267579793930054},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3831775486469269},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3284558355808258},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25158682465553284},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19764280319213867},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.08875918388366699},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.05482819676399231},{"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/tac.2025.3550074","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2025.3550074","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1109/tac.2025.3550074","is_oa":true,"landing_page_url":"https://doi.org/10.1109/tac.2025.3550074","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3360497695","display_name":null,"funder_award_id":"ERC","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3670389706","display_name":null,"funder_award_id":"C-NORA","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6638087972","display_name":null,"funder_award_id":"101088147","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W203646022","https://openalex.org/W357046174","https://openalex.org/W1504222318","https://openalex.org/W1606157354","https://openalex.org/W1990834757","https://openalex.org/W2019091709","https://openalex.org/W2057885843","https://openalex.org/W2064085278","https://openalex.org/W2099589402","https://openalex.org/W2108011767","https://openalex.org/W2130181194","https://openalex.org/W2140122171","https://openalex.org/W2148232499","https://openalex.org/W2158970797","https://openalex.org/W2165755353","https://openalex.org/W2482021336","https://openalex.org/W2499641798","https://openalex.org/W2791510101","https://openalex.org/W2944894127","https://openalex.org/W2994113221","https://openalex.org/W3015878641","https://openalex.org/W3045642293","https://openalex.org/W3175552343","https://openalex.org/W3175585712","https://openalex.org/W3209307638","https://openalex.org/W3216165517","https://openalex.org/W4205460823","https://openalex.org/W4220888465","https://openalex.org/W4312607148","https://openalex.org/W4315489213","https://openalex.org/W4321484105","https://openalex.org/W4390224269","https://openalex.org/W4390721176","https://openalex.org/W4390848502","https://openalex.org/W4391020320","https://openalex.org/W4402159719","https://openalex.org/W4405031180"],"related_works":["https://openalex.org/W2099991058","https://openalex.org/W2066764747","https://openalex.org/W161810272","https://openalex.org/W144405564","https://openalex.org/W3118471514","https://openalex.org/W2969693569","https://openalex.org/W2609974967","https://openalex.org/W1970322054","https://openalex.org/W2069661783","https://openalex.org/W1978474130"],"abstract_inverted_index":{"In":[0,215],"this":[1,234],"article,":[2],"we":[3,217],"establish":[4,219],"that":[5,62,81,118,122,150,163,165],"stabilization":[6,39,69,92],"of":[7,10,23,30,40,48,53,70,93,101,111,115,167,169,179,181,193,210,241],"a":[8,18,31,41,94,112,138,160],"class":[9],"linear,":[11],"hyperbolic":[12],"partial":[13],"differential":[14],"equations":[15],"(PDEs)":[16],"with":[17,142,176],"large":[19],"(nevertheless":[20],"finite)":[21],"number":[22,47,178],"components,":[24],"can":[25,74,236],"be":[26,75,237],"achieved":[27,59],"via":[28],"employment":[29],"backstepping-based":[32,245],"control":[33,246],"law,":[34],"which":[35,203],"is":[36,58,84,119],"constructed":[37,67,90,189,206],"for":[38,68,91,239,248],"continuum":[42,95,154,195,231],"version":[43,96],"(i.e.,":[44],"as":[45],"the":[46,54,63,71,87,102,126,133,153,177,182,186,191,194,200,208,211,220,223,226],"components":[49,180],"tends":[50],"to":[51,144,199,225],"infinity)":[52],"PDE":[55,104,183,250],"system.":[56,105,214],"This":[57],"by":[60,86],"proving":[61],"exact":[64,127],"backstepping":[65,88,116,128,155,171],"kernels,":[66],"large-scale":[72,135,213,227,249],"system,":[73],"approximated":[76],"(in":[77],"certain":[78],"sense":[79],"such":[80,121],"exponential":[82],"stability":[83],"preserved)":[85],"kernels":[89,117,129,172,187],"(essentially":[97],"an":[98,145],"infinite":[99],"ensemble)":[100],"original":[103],"The":[106],"proof":[107],"relies":[108],"on":[109,132,190,207],"construction":[110],"convergent":[113],"sequence":[114],"defined":[120],"each":[123],"kernel":[124,156],"matches":[125],"(derived":[130],"based":[131],"original,":[134,212],"system),":[136],"in":[137,197,202],"piecewise":[139],"constant":[140],"manner":[141],"respect":[143],"ensemble":[146],"variable;":[147],"while":[148],"showing":[149],"they":[151,204],"satisfy":[152],"equations.":[157],"We":[158],"present":[159],"numerical":[161],"example":[162],"reveals":[164],"complexity":[166],"computation":[168],"stabilizing":[170,244],"may":[173],"not":[174],"scale":[175],"state,":[184],"when":[185],"are":[188,205],"basis":[192,209],"version,":[196],"contrast":[198],"case":[201],"addition,":[216],"formally":[218],"connection":[221],"between":[222],"solutions":[224],"system":[228],"and":[229],"its":[230],"counterpart.":[232],"Thus,":[233],"approach":[235],"useful":[238],"design":[240],"computationally":[242],"tractable,":[243],"laws":[247],"systems.":[251]},"counts_by_year":[{"year":2025,"cited_by_count":4}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}