{"id":"https://openalex.org/W4417142980","doi":"https://doi.org/10.48550/arxiv.2512.05547","title":"Constructive boundary observer-based control of high-dimensional semilinear heat equations","display_name":"Constructive boundary observer-based control of high-dimensional semilinear heat equations","publication_year":2025,"publication_date":"2025-12-05","ids":{"openalex":"https://openalex.org/W4417142980","doi":"https://doi.org/10.48550/arxiv.2512.05547"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2512.05547","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.05547","pdf_url":"https://arxiv.org/pdf/2512.05547","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2512.05547","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100399559","display_name":"Pengfei Wang","orcid":"https://orcid.org/0000-0002-4218-5467"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Wang, Pengfei","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007830129","display_name":"Emilia Fridman","orcid":"https://orcid.org/0000-0002-8773-9494"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fridman, Emilia","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100399559"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"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":0.9951000213623047,"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":0.9951000213623047,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.0010999999940395355,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.0005000000237487257,"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/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.7799000144004822},{"id":"https://openalex.org/keywords/multiplicative-noise","display_name":"Multiplicative noise","score":0.6355000138282776},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.6266999840736389},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5777999758720398},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5325999855995178},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5092999935150146},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.4616999924182892},{"id":"https://openalex.org/keywords/heat-equation","display_name":"Heat equation","score":0.45989999175071716},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.43149998784065247}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.7799000144004822},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.743399977684021},{"id":"https://openalex.org/C18015164","wikidata":"https://www.wikidata.org/wiki/Q6935000","display_name":"Multiplicative noise","level":5,"score":0.6355000138282776},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.6266999840736389},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5777999758720398},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5325999855995178},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5092999935150146},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.4616999924182892},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.45989999175071716},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4496999979019165},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.4269999861717224},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.4050000011920929},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.40139999985694885},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39410001039505005},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.38760000467300415},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.3817000091075897},{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.36890000104904175},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.35850000381469727},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.34619998931884766},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.33959999680519104},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.3393999934196472},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.30640000104904175},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.27619999647140503},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.2605000138282776},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.25600001215934753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2512.05547","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.05547","pdf_url":"https://arxiv.org/pdf/2512.05547","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2512.05547","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2512.05547","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2512.05547","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2512.05547","pdf_url":"https://arxiv.org/pdf/2512.05547","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"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],"presents":[2],"a":[3,49,60],"constructive":[4],"finite-dimensional":[5],"output-feedback":[6],"design":[7,78],"for":[8,108,125,131,136],"semilinear":[9],"$M$-dimensional":[10],"($M\\geq":[11],"2$)":[12],"heat":[13],"equations":[14],"with":[15,89],"boundary":[16,64],"actuation":[17],"and":[18,70,114,128,138,144],"sensing.":[19],"A":[20],"key":[21],"challenge":[22],"in":[23],"high":[24],"dimensions":[25],"is":[26],"the":[27,32,63,66,71,77,83,86,97,110,120,142],"slower":[28],"growth":[29],"rate":[30],"of":[31,38,52,62,85,146],"Laplacian":[33],"eigenvalues.":[34],"The":[35],"novel":[36],"features":[37],"our":[39,147],"modal-decomposition-based":[40],"design,":[41],"which":[42],"allows":[43],"to":[44,91],"enlarge":[45],"Lipschitz":[46,116],"constants,":[47],"include":[48],"larger":[50],"class":[51],"shape":[53],"functions":[54],"that":[55,118],"may":[56],"be":[57],"distributed":[58],"over":[59],"part":[61],"only,":[65],"corresponding":[67],"lifting":[68],"transformation":[69],"full-order":[72],"controller":[73],"gain":[74],"found":[75],"from":[76],"LMIs.":[79],"We":[80],"further":[81],"analyze":[82],"robustness":[84],"closed-loop":[87],"system":[88],"respect":[90],"either":[92],"multiplicative":[93,126],"noise":[94,101,127],"(vanishing":[95],"at":[96],"origin)":[98],"or":[99],"additive":[100,132],"(persistent).":[102],"Effective":[103],"LMI":[104],"conditions":[105],"are":[106],"provided":[107],"specifying":[109],"minimal":[111],"observer":[112],"dimension":[113],"maximal":[115],"constants":[117],"preserve":[119],"stability":[121,124,130],"(mean-square":[122],"exponential":[123],"noise-to-state":[129],"noise).":[133],"Numerical":[134],"examples":[135],"2D":[137],"3D":[139],"cases":[140],"demonstrate":[141],"efficacy":[143],"advantages":[145],"method.":[148]},"counts_by_year":[],"updated_date":"2026-03-07T16:01:11.037858","created_date":"2025-12-09T00:00:00"}
