{"id":"https://openalex.org/W2133141924","doi":"https://doi.org/10.1109/acc.2006.1655329","title":"Boundary predictive control of parabolic PDEs","display_name":"Boundary predictive control of parabolic PDEs","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2133141924","doi":"https://doi.org/10.1109/acc.2006.1655329","mag":"2133141924"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2006.1655329","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2006.1655329","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 American Control Conference","raw_type":"proceedings-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/A5031561953","display_name":"Stevan Dubljevi\u0107","orcid":"https://orcid.org/0000-0002-1889-1599"},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Dubljevic","raw_affiliation_strings":["Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA, USA","Dept. of Chem. & Biomolecular Eng., California Univ., Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Dept. of Chem. & Biomolecular Eng., California Univ., Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5063789547","display_name":"P.D. Christofides","orcid":null},"institutions":[{"id":"https://openalex.org/I161318765","display_name":"University of California, Los Angeles","ror":"https://ror.org/046rm7j60","country_code":"US","type":"education","lineage":["https://openalex.org/I161318765"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P.D. Christofides","raw_affiliation_strings":["Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA, USA","Dept. of Chem. & Biomolecular Eng., California Univ., Los Angeles, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]},{"raw_affiliation_string":"Dept. of Chem. & Biomolecular Eng., California Univ., Los Angeles, CA, USA","institution_ids":["https://openalex.org/I161318765"]}]}],"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":10,"citation_normalized_percentile":{"value":0.1185905,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"8 pp.","last_page":"8 pp."},"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":0.9962999820709229,"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":0.9962999820709229,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.984499990940094,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9728000164031982,"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/model-predictive-control","display_name":"Model predictive control","score":0.8316689729690552},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6657283306121826},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6627143621444702},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.637413740158081},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5835844278335571},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5682871341705322},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5597058534622192},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5164649486541748},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5057933330535889},{"id":"https://openalex.org/keywords/distributed-parameter-system","display_name":"Distributed parameter system","score":0.45861223340034485},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.44934356212615967},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.4273446798324585},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38330018520355225},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36732035875320435},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3567195236682892},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32566651701927185},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.16737809777259827},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07715445756912231}],"concepts":[{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.8316689729690552},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6657283306121826},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6627143621444702},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.637413740158081},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5835844278335571},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5682871341705322},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5597058534622192},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5164649486541748},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5057933330535889},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.45861223340034485},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.44934356212615967},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.4273446798324585},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38330018520355225},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36732035875320435},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3567195236682892},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32566651701927185},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.16737809777259827},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07715445756912231},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2006.1655329","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2006.1655329","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2006 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W40130861","https://openalex.org/W1538686203","https://openalex.org/W1560060148","https://openalex.org/W1966686724","https://openalex.org/W1966922258","https://openalex.org/W1967322671","https://openalex.org/W1978956894","https://openalex.org/W1986393509","https://openalex.org/W1990595104","https://openalex.org/W1997138061","https://openalex.org/W2001018729","https://openalex.org/W2019341732","https://openalex.org/W2026879762","https://openalex.org/W2027518125","https://openalex.org/W2040278456","https://openalex.org/W2057931445","https://openalex.org/W2066278848","https://openalex.org/W2073787051","https://openalex.org/W2078746189","https://openalex.org/W2081952592","https://openalex.org/W2082009002","https://openalex.org/W2082452351","https://openalex.org/W2090167557","https://openalex.org/W2102602923","https://openalex.org/W2104412804","https://openalex.org/W2111273871","https://openalex.org/W2117463657","https://openalex.org/W2140563796","https://openalex.org/W2154140920","https://openalex.org/W2159148686","https://openalex.org/W2170716704","https://openalex.org/W2180472741","https://openalex.org/W2783350696","https://openalex.org/W4213298939","https://openalex.org/W6675602286"],"related_works":["https://openalex.org/W1967450583","https://openalex.org/W2066764747","https://openalex.org/W2354582784","https://openalex.org/W2385175414","https://openalex.org/W203831624","https://openalex.org/W2083817219","https://openalex.org/W4244681779","https://openalex.org/W2264582182","https://openalex.org/W3047860677","https://openalex.org/W4399084239"],"abstract_inverted_index":{"This":[0],"work":[1],"focuses":[2],"on":[3],"predictive":[4,38,91],"control":[5,15,39,74,79],"of":[6,28,62,89],"linear":[7,64],"parabolic":[8,65],"partial":[9],"differential":[10],"equations":[11],"(PDEs)":[12],"with":[13,67],"boundary":[14,73],"actuation":[16],"subject":[17,75],"to":[18,46,76,83],"input":[19],"and":[20,36,43,49,71,78,87],"state":[21,31,70,77],"constraints.":[22],"Under":[23],"the":[24,29,53,85,90],"assumption":[25],"that":[26],"measurements":[27],"PDE":[30,66],"are":[32,41],"available,":[33],"various":[34],"finite-dimensional":[35],"infinite-dimensional":[37,54],"formulations":[40],"presented":[42],"their":[44],"ability":[45],"enforce":[47],"stability":[48],"constraint":[50],"satisfaction":[51],"in":[52],"closed-loop":[55],"system":[56],"is":[57,81],"analyzed.":[58],"A":[59],"numerical":[60],"example":[61],"a":[63],"unstable":[68],"steady":[69],"flux":[72],"constraints":[80],"used":[82],"demonstrate":[84],"implementation":[86],"effectiveness":[88],"controllers":[92]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}