{"id":"https://openalex.org/W1559174401","doi":"https://doi.org/10.1109/acc.2015.7171998","title":"Output stabilization of boundary-controlled parabolic PDEs via gradient-based dynamic optimization","display_name":"Output stabilization of boundary-controlled parabolic PDEs via gradient-based dynamic optimization","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1559174401","doi":"https://doi.org/10.1109/acc.2015.7171998","mag":"1559174401"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2015.7171998","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7171998","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://espace.curtin.edu.au/bitstream/20.500.11937/15628/2/228364_228364.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068707928","display_name":"Zhigang Ren","orcid":"https://orcid.org/0000-0002-0913-0130"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]},{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]},{"id":"https://openalex.org/I4391767838","display_name":"State Key Laboratory of Industrial Control Technology","ror":"https://ror.org/03a33a786","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767838","https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhigang Ren","raw_affiliation_strings":["Zhejiang University, Hangzhou, Zhejiang, CN","State Key Laboratory of Industrial Control Technology and the Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Zhejiang University, Hangzhou, Zhejiang, CN","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"State Key Laboratory of Industrial Control Technology and the Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I55712492","https://openalex.org/I4391767838"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050543156","display_name":"Chao Xu","orcid":"https://orcid.org/0000-0002-2759-6364"},"institutions":[{"id":"https://openalex.org/I4391767838","display_name":"State Key Laboratory of Industrial Control Technology","ror":"https://ror.org/03a33a786","country_code":null,"type":"facility","lineage":["https://openalex.org/I4391767838","https://openalex.org/I76130692"]},{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]},{"id":"https://openalex.org/I55712492","display_name":"Zhejiang University of Technology","ror":"https://ror.org/02djqfd08","country_code":"CN","type":"education","lineage":["https://openalex.org/I55712492"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chao Xu","raw_affiliation_strings":["Zhejiang University, Hangzhou, Zhejiang, CN","State Key Laboratory of Industrial Control Technology and the Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China"],"affiliations":[{"raw_affiliation_string":"Zhejiang University, Hangzhou, Zhejiang, CN","institution_ids":["https://openalex.org/I76130692"]},{"raw_affiliation_string":"State Key Laboratory of Industrial Control Technology and the Institute of Cyber-Systems and Control, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I55712492","https://openalex.org/I4391767838"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5023320871","display_name":"Qun Lin","orcid":"https://orcid.org/0000-0003-0209-6424"},"institutions":[{"id":"https://openalex.org/I205640436","display_name":"Curtin University","ror":"https://ror.org/02n415q13","country_code":"AU","type":"education","lineage":["https://openalex.org/I205640436"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Qun Lin","raw_affiliation_strings":["Curtin University, Perth, WA, AU","Department of Mathematics and Statistics, Curtin University , Perth, Australia"],"affiliations":[{"raw_affiliation_string":"Curtin University, Perth, WA, AU","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Curtin University , Perth, Australia","institution_ids":["https://openalex.org/I205640436"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066144982","display_name":"Ryan Loxton","orcid":"https://orcid.org/0000-0001-9821-2885"},"institutions":[{"id":"https://openalex.org/I205640436","display_name":"Curtin University","ror":"https://ror.org/02n415q13","country_code":"AU","type":"education","lineage":["https://openalex.org/I205640436"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ryan Loxton","raw_affiliation_strings":["Curtin University, Perth, WA, AU","Department of Mathematics and Statistics, Curtin University , Perth, Australia"],"affiliations":[{"raw_affiliation_string":"Curtin University, Perth, WA, AU","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematics and Statistics, Curtin University , Perth, Australia","institution_ids":["https://openalex.org/I205640436"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5068707928"],"corresponding_institution_ids":["https://openalex.org/I4391767838","https://openalex.org/I55712492","https://openalex.org/I76130692"],"apc_list":null,"apc_paid":null,"fwci":0.3366,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62388436,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"4257","last_page":"4262"},"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":0.9864000082015991,"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":0.9864000082015991,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9861000180244446,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9851999878883362,"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/control-theory","display_name":"Control theory (sociology)","score":0.5633835792541504},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5443708896636963},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4275493621826172},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2211451530456543},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21343019604682922},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.11112019419670105}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5633835792541504},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5443708896636963},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4275493621826172},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2211451530456543},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21343019604682922},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.11112019419670105},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/acc.2015.7171998","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7171998","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","raw_type":"proceedings-article"},{"id":"pmh:oai:espace.curtin.edu.au:20.500.11937/15628","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11937/15628","pdf_url":"https://espace.curtin.edu.au/bitstream/20.500.11937/15628/2/228364_228364.pdf","source":{"id":"https://openalex.org/S4306401790","display_name":"eSpace (Curtin University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205640436","host_organization_name":"Curtin University","host_organization_lineage":["https://openalex.org/I205640436"],"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":"Conference Paper"}],"best_oa_location":{"id":"pmh:oai:espace.curtin.edu.au:20.500.11937/15628","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.11937/15628","pdf_url":"https://espace.curtin.edu.au/bitstream/20.500.11937/15628/2/228364_228364.pdf","source":{"id":"https://openalex.org/S4306401790","display_name":"eSpace (Curtin University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205640436","host_organization_name":"Curtin University","host_organization_lineage":["https://openalex.org/I205640436"],"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":"Conference Paper"},"sustainable_development_goals":[{"score":0.6000000238418579,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1559174401.pdf","grobid_xml":"https://content.openalex.org/works/W1559174401.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W563110697","https://openalex.org/W568671212","https://openalex.org/W1498121547","https://openalex.org/W1538686203","https://openalex.org/W1901119619","https://openalex.org/W1966249877","https://openalex.org/W1967563465","https://openalex.org/W1988476486","https://openalex.org/W1990039295","https://openalex.org/W2016805534","https://openalex.org/W2052849686","https://openalex.org/W2060542320","https://openalex.org/W2067019787","https://openalex.org/W2068571038","https://openalex.org/W2069318967","https://openalex.org/W2078609652","https://openalex.org/W2088233472","https://openalex.org/W2091562669","https://openalex.org/W2092070018","https://openalex.org/W2104939087","https://openalex.org/W2106829923","https://openalex.org/W2113418259","https://openalex.org/W2115539225","https://openalex.org/W2118060962","https://openalex.org/W2146562920","https://openalex.org/W2150326502","https://openalex.org/W2153356113","https://openalex.org/W2158953580","https://openalex.org/W2165346582","https://openalex.org/W2499641798","https://openalex.org/W2963553414","https://openalex.org/W2974720244","https://openalex.org/W4292027189","https://openalex.org/W6615631860","https://openalex.org/W6639799579","https://openalex.org/W6697178167"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052","https://openalex.org/W4402327032","https://openalex.org/W2382290278"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,49],"new":[4,115],"control":[5,25,100,140,150],"synthesis":[6,141],"approach":[7,116],"for":[8,143],"the":[9,19,22,38,63,70,80,119,132,138,148],"stabilization":[10,82],"of":[11,69,72,113],"boundary-controlled":[12,144],"parabolic":[13,145],"partial":[14],"differential":[15],"equations":[16],"(PDEs).":[17],"In":[18,136],"proposed":[20],"approach,":[21],"optimal":[23,98],"boundary":[24,99],"is":[26,101,117,122],"expressed":[27],"in":[28,67,123],"integral":[29],"state":[30,56],"feedback":[31],"form":[32,125],"with":[33],"quadratic":[34,94],"kernel":[35,58],"function,":[36],"where":[37],"quadratic's":[39],"coefficients":[40],"are":[41],"decision":[42],"variables":[43],"to":[44,53,103],"be":[45,85,128],"optimized.":[46],"We":[47],"introduce":[48],"system":[50],"cost":[51,64],"functional":[52],"penalize":[54],"both":[55],"and":[57,60,126,151,158],"magnitude,":[59],"then":[61],"derive":[62],"functional's":[65],"gradient":[66],"terms":[68],"solution":[71],"an":[73],"auxiliary":[74],"\u201ccostate\u201d":[75],"PDE.":[76],"On":[77],"this":[78],"basis,":[79],"output":[81],"problem":[83],"can":[84,127],"solved":[86,129],"using":[87,131],"gradient-based":[88],"optimization":[89],"techniques":[90],"such":[91],"as":[92],"sequential":[93],"programming.":[95],"The":[96,110],"resulting":[97],"guaranteed":[102],"yield":[104],"closed-loop":[105],"stability":[106],"under":[107],"mild":[108],"conditions.":[109],"primary":[111],"advantage":[112],"our":[114],"that":[118],"costate":[120],"PDE":[121],"standard":[124],"easily":[130],"finite":[133],"difference":[134],"method.":[135],"contrast,":[137],"traditional":[139],"approaches":[142],"PDEs":[146],"(i.e.,":[147],"LQ":[149],"backstepping":[152],"approaches)":[153],"require":[154],"solving":[155],"non-standard":[156],"Riccati-type":[157],"Klein-Gorden-type":[159],"PDEs.":[160]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}