{"id":"https://openalex.org/W2133711647","doi":"https://doi.org/10.1109/acc.2011.5991343","title":"Bochner integrable solutions to Riccati partial differential equations and optimal sensor placement","display_name":"Bochner integrable solutions to Riccati partial differential equations and optimal sensor placement","publication_year":2011,"publication_date":"2011-06-01","ids":{"openalex":"https://openalex.org/W2133711647","doi":"https://doi.org/10.1109/acc.2011.5991343","mag":"2133711647"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2011.5991343","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2011.5991343","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 American Control Conference","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/A5102791907","display_name":"John A. Burns","orcid":"https://orcid.org/0000-0003-1840-927X"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. A. Burns","raw_affiliation_strings":["Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA","Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]},{"raw_affiliation_string":"Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg, USA","institution_ids":["https://openalex.org/I859038795"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5001640899","display_name":"Carlos N. Rautenberg","orcid":"https://orcid.org/0000-0001-9497-9296"},"institutions":[{"id":"https://openalex.org/I859038795","display_name":"Virginia Tech","ror":"https://ror.org/02smfhw86","country_code":"US","type":"education","lineage":["https://openalex.org/I859038795"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. N. Rautenberg","raw_affiliation_strings":["Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA","Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Interdisciplinary Center for Applied Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA","institution_ids":["https://openalex.org/I859038795"]},{"raw_affiliation_string":"Interdisciplinary Center for Applied Mathematics, Virginia Tech, Blacksburg, USA","institution_ids":["https://openalex.org/I859038795"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I859038795"],"apc_list":null,"apc_paid":null,"fwci":0.5823,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66360899,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"2368","last_page":"2373"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9993000030517578,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/integrable-system","display_name":"Integrable system","score":0.6967318654060364},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6393152475357056},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5902847647666931},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.569650411605835},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5160341262817383},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.511216402053833},{"id":"https://openalex.org/keywords/trace","display_name":"TRACE (psycholinguistics)","score":0.46938464045524597},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.44356346130371094},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35820549726486206},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3318086862564087},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30071690678596497}],"concepts":[{"id":"https://openalex.org/C200741047","wikidata":"https://www.wikidata.org/wiki/Q1957758","display_name":"Integrable system","level":2,"score":0.6967318654060364},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6393152475357056},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5902847647666931},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.569650411605835},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5160341262817383},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.511216402053833},{"id":"https://openalex.org/C75291252","wikidata":"https://www.wikidata.org/wiki/Q1315756","display_name":"TRACE (psycholinguistics)","level":2,"score":0.46938464045524597},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.44356346130371094},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35820549726486206},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3318086862564087},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30071690678596497},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2011.5991343","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2011.5991343","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2011 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W105372955","https://openalex.org/W340087540","https://openalex.org/W576215968","https://openalex.org/W1527296550","https://openalex.org/W1981420955","https://openalex.org/W1985953691","https://openalex.org/W1995018531","https://openalex.org/W1995492482","https://openalex.org/W2029996848","https://openalex.org/W2041325915","https://openalex.org/W2063819119","https://openalex.org/W2110115424","https://openalex.org/W2135957782"],"related_works":["https://openalex.org/W2044787408","https://openalex.org/W4249228129","https://openalex.org/W2086585817","https://openalex.org/W4394635378","https://openalex.org/W2019140719","https://openalex.org/W155593081","https://openalex.org/W3104927070","https://openalex.org/W1506619710","https://openalex.org/W2738038633","https://openalex.org/W2052607948"],"abstract_inverted_index":{"In":[0],"this":[1,77],"paper":[2],"we":[3],"provide":[4],"sufficient":[5],"conditions":[6],"to":[7,11,63,70,82,105],"ensure":[8,64],"that":[9,33],"solutions":[10],"the":[12,25,65,107],"time":[13],"varying":[14],"Riccati":[15],"partial":[16],"differential":[17],"equations":[18],"are":[19,98,103],"Bochner":[20,34],"integrable":[21],"with":[22],"range":[23],"in":[24],"space":[26],"of":[27,67],"trace":[28],"class":[29],"operators.":[30],"The":[31],"fact":[32],"integrals":[35],"can":[36,54,79],"be":[37,56,80],"uniformly":[38],"approximated":[39],"by":[40],"simple":[41],"functions":[42],"provides":[43],"a":[44,88],"basis":[45],"for":[46,58,87],"obtaining":[47],"bounds":[48,53],"on":[49,93],"integration":[50],"errors.":[51],"These":[52],"then":[55],"used":[57,69],"rigorous":[59],"numerical":[60,101],"analysis":[61],"and":[62,100],"convergence":[66],"algorithms":[68],"compute":[71],"approximate":[72],"solutions.":[73],"We":[74],"demonstrate":[75],"how":[76],"result":[78],"employed":[81],"develop":[83],"convergent":[84],"computational":[85],"methods":[86],"sensor":[89],"placement":[90],"problem":[91],"based":[92],"optimal":[94],"filtering.":[95],"Theoretical":[96],"results":[97],"presented":[99],"examples":[102],"given":[104],"illustrate":[106],"ideas.":[108]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T14:22:42.915294","created_date":"2025-10-10T00:00:00"}