{"id":"https://openalex.org/W1578193925","doi":"https://doi.org/10.23919/ecc.2009.7074689","title":"RBF-based 2D optimal spatial control of the 3D reaction-convection-diffusion equation","display_name":"RBF-based 2D optimal spatial control of the 3D reaction-convection-diffusion equation","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W1578193925","doi":"https://doi.org/10.23919/ecc.2009.7074689","mag":"1578193925"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2009.7074689","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2009.7074689","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5063096526","display_name":"Masako Kishida","orcid":"https://orcid.org/0000-0001-7958-1001"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Masako Kishida","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, Urbana, IL, USA","University of Illinois at Urbana-Champaign, Urbana 61801, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, Urbana 61801, USA","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083684552","display_name":"Richard D. Braatz","orcid":"https://orcid.org/0000-0003-4304-3484"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard D. Braatz","raw_affiliation_strings":["University of Illinois at Urbana-Champaign, Urbana, IL, USA","University of Illinois at Urbana-Champaign, Urbana 61801, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]},{"raw_affiliation_string":"University of Illinois at Urbana-Champaign, Urbana 61801, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I157725225"],"apc_list":null,"apc_paid":null,"fwci":1.7331,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.8350382,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"1949","last_page":"1954"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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":0.9979000091552734,"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/optimal-control","display_name":"Optimal control","score":0.7388028502464294},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.6569628715515137},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6278471350669861},{"id":"https://openalex.org/keywords/moment","display_name":"Moment (physics)","score":0.6075621843338013},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5833725929260254},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.5674307942390442},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5242507457733154},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4920024573802948},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.47274646162986755},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.470379501581192},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.4473240077495575},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.44359642267227173},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.4350174367427826},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3988010287284851},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3862989544868469},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3669970631599426},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.265644907951355},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21182841062545776},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.13490641117095947},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.13488838076591492},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11916646361351013},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08642825484275818}],"concepts":[{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7388028502464294},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.6569628715515137},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6278471350669861},{"id":"https://openalex.org/C179254644","wikidata":"https://www.wikidata.org/wiki/Q13222844","display_name":"Moment (physics)","level":2,"score":0.6075621843338013},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5833725929260254},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.5674307942390442},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5242507457733154},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4920024573802948},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.47274646162986755},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.470379501581192},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.4473240077495575},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.44359642267227173},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.4350174367427826},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3988010287284851},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3862989544868469},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3669970631599426},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.265644907951355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21182841062545776},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.13490641117095947},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.13488838076591492},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11916646361351013},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08642825484275818},{"id":"https://openalex.org/C21547014","wikidata":"https://www.wikidata.org/wiki/Q1423657","display_name":"Operations management","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2009.7074689","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2009.7074689","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1494068645","https://openalex.org/W1498121547","https://openalex.org/W1579878850","https://openalex.org/W1593833610","https://openalex.org/W1967416910","https://openalex.org/W1996818420","https://openalex.org/W1997283008","https://openalex.org/W2014311013","https://openalex.org/W2029198995","https://openalex.org/W2033552200","https://openalex.org/W2040135606","https://openalex.org/W2041304886","https://openalex.org/W2044101375","https://openalex.org/W2047090868","https://openalex.org/W2047161049","https://openalex.org/W2056304970","https://openalex.org/W2058527798","https://openalex.org/W2062398123","https://openalex.org/W2069470631","https://openalex.org/W2102116693","https://openalex.org/W2103496339","https://openalex.org/W2113442785","https://openalex.org/W2134298283","https://openalex.org/W2150535417","https://openalex.org/W2153425320"],"related_works":["https://openalex.org/W2441614350","https://openalex.org/W1994822208","https://openalex.org/W603561220","https://openalex.org/W2124138615","https://openalex.org/W1981721685","https://openalex.org/W2068505497","https://openalex.org/W2370498728","https://openalex.org/W4366196986","https://openalex.org/W2072834359","https://openalex.org/W4242356838"],"abstract_inverted_index":{"Solving":[0],"optimal":[1,39,82,91],"control":[2,40,83,92,101],"problems":[3,41],"for":[4,27,42,46],"spatially-distributed":[5,44],"systems":[6],"with":[7,31],"multiple":[8],"spatial":[9,76,109],"dimensions":[10],"can":[11],"be":[12],"computationally":[13],"expensive.":[14],"A":[15,62],"numerical":[16],"algorithm":[17],"is":[18,36,50,65,87],"proposed":[19],"that":[20],"combines":[21],"a":[22,53],"radial":[23],"basis":[24],"function":[25],"expansion":[26],"the":[28,48,56,66,73,79,90,94,100],"target":[29,104],"trajectory":[30],"moment":[32],"analysis.":[33],"The":[34],"approach":[35,86],"applicable":[37],"to":[38,72,89],"linear":[43],"systems,":[45],"which":[47,99],"solution":[49],"expressed":[51],"as":[52],"convolution":[54],"of":[55,68,75,93],"system's":[57],"kernel":[58],"and":[59,103],"its":[60,69],"inputs.":[61],"novel":[63],"feature":[64],"insensitivity":[67],"computational":[70],"cost":[71],"sharpness":[74],"variations":[77],"in":[78,98],"state":[80],"or":[81],"fields.":[84,110],"This":[85],"applied":[88],"three-dimensional":[95],"reaction-convection-diffusion":[96],"equation":[97],"input":[102],"are":[105],"defined":[106],"over":[107],"two-dimensional":[108]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}
