{"id":"https://openalex.org/W1560557268","doi":"https://doi.org/10.1109/acc.2015.7171128","title":"Operator theoretic approach to the optimal distributed control problem for spatially invariant systems","display_name":"Operator theoretic approach to the optimal distributed control problem for spatially invariant systems","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1560557268","doi":"https://doi.org/10.1109/acc.2015.7171128","mag":"1560557268"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2015.7171128","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7171128","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024483587","display_name":"Seddik M. Djouadi","orcid":"https://orcid.org/0000-0002-5211-1939"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Seddik M. Djouadi","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN","Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville 37996 (United States)"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville 37996 (United States)","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5012002316","display_name":"Jin Dong","orcid":"https://orcid.org/0000-0002-5753-1588"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jin Dong","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN","Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville 37996 (United States)"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville, TN","institution_ids":["https://openalex.org/I75027704"]},{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville 37996 (United States)","institution_ids":["https://openalex.org/I75027704"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024483587"],"corresponding_institution_ids":["https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":1.9493,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.83860126,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"44","issue":null,"first_page":"2613","last_page":"2618"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.95660001039505,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.95660001039505,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9495999813079834,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9362999796867371,"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/tensor-product","display_name":"Tensor product","score":0.7378215193748474},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7163381576538086},{"id":"https://openalex.org/keywords/reflexive-operator-algebra","display_name":"Reflexive operator algebra","score":0.5846519470214844},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.504125714302063},{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.4960964620113373},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.46346914768218994},{"id":"https://openalex.org/keywords/product-topology","display_name":"Product topology","score":0.45721057057380676},{"id":"https://openalex.org/keywords/tensor-product-of-hilbert-spaces","display_name":"Tensor product of Hilbert spaces","score":0.42869603633880615},{"id":"https://openalex.org/keywords/finite-rank-operator","display_name":"Finite-rank operator","score":0.41662511229515076},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.3986265957355499},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.35889554023742676},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.335310697555542},{"id":"https://openalex.org/keywords/compact-operator","display_name":"Compact operator","score":0.2981567978858948},{"id":"https://openalex.org/keywords/tensor-contraction","display_name":"Tensor contraction","score":0.24793818593025208},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21920788288116455},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.12060049176216125}],"concepts":[{"id":"https://openalex.org/C51255310","wikidata":"https://www.wikidata.org/wiki/Q1163016","display_name":"Tensor product","level":2,"score":0.7378215193748474},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7163381576538086},{"id":"https://openalex.org/C16324678","wikidata":"https://www.wikidata.org/wiki/Q7307359","display_name":"Reflexive operator algebra","level":4,"score":0.5846519470214844},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.504125714302063},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.4960964620113373},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.46346914768218994},{"id":"https://openalex.org/C123222754","wikidata":"https://www.wikidata.org/wiki/Q1070472","display_name":"Product topology","level":2,"score":0.45721057057380676},{"id":"https://openalex.org/C93776189","wikidata":"https://www.wikidata.org/wiki/Q1404488","display_name":"Tensor product of Hilbert spaces","level":4,"score":0.42869603633880615},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.41662511229515076},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.3986265957355499},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.35889554023742676},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.335310697555542},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.2981567978858948},{"id":"https://openalex.org/C124007464","wikidata":"https://www.wikidata.org/wiki/Q428091","display_name":"Tensor contraction","level":3,"score":0.24793818593025208},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21920788288116455},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.12060049176216125},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2015.7171128","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7171128","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1509568713","https://openalex.org/W1534416612","https://openalex.org/W1582706191","https://openalex.org/W1604745759","https://openalex.org/W1971186339","https://openalex.org/W1979171951","https://openalex.org/W1988095001","https://openalex.org/W1999190365","https://openalex.org/W2001874077","https://openalex.org/W2027584575","https://openalex.org/W2061378078","https://openalex.org/W2105532855","https://openalex.org/W2111836897","https://openalex.org/W2115356325","https://openalex.org/W2118082066","https://openalex.org/W2129891269","https://openalex.org/W2136598296","https://openalex.org/W2137125234","https://openalex.org/W2146445863","https://openalex.org/W2146890818","https://openalex.org/W2147539438","https://openalex.org/W2151063922","https://openalex.org/W2151582423","https://openalex.org/W2158983145","https://openalex.org/W2166103243","https://openalex.org/W2166778103","https://openalex.org/W2169488608","https://openalex.org/W3101538765","https://openalex.org/W3142756138","https://openalex.org/W6681857541","https://openalex.org/W6682089242"],"related_works":["https://openalex.org/W132488082","https://openalex.org/W2951694249","https://openalex.org/W4205205188","https://openalex.org/W2810638431","https://openalex.org/W1992711251","https://openalex.org/W2171365950","https://openalex.org/W2496100290","https://openalex.org/W1968139066","https://openalex.org/W1983099806","https://openalex.org/W4242949454"],"abstract_inverted_index":{"This":[0,29],"paper":[1,117],"considers":[2],"the":[3,19,31,36,39,58,93,105,119,125],"problem":[4,20],"of":[5,9,18,25,47,84,109,128],"optimal":[6,94],"distributed":[7,95],"control":[8,96,122],"spatially":[10,99],"invariant":[11,100],"systems.":[12],"The":[13,74,112],"Banach":[14],"space":[15,76],"duality":[16],"structure":[17],"is":[21,102],"characterized":[22],"in":[23,45,82,115],"terms":[24,46,83],"tensor":[26,69,75,90,129],"product":[27,130],"spaces.":[28,49,131],"complements":[30],"prior":[32],"study":[33],"undertaken":[34],"by":[35,88],"authors,":[37],"where":[38],"dual":[40],"and":[41,60,71,124],"pre-dual":[42],"formulations":[43],"were":[44],"abstract":[48],"Here,":[50],"we":[51],"show":[52],"that":[53],"these":[54],"spaces":[55,70],"together":[56],"with":[57],"pre-annihilator":[59],"annihilator":[61],"subspaces":[62],"can":[63],"be":[64],"realized":[65],"explicitly":[66],"as":[67],"specific":[68],"subspaces,":[72],"respectively.":[73],"formulation":[77],"leads":[78],"to":[79,104],"a":[80,89],"solution":[81],"an":[85],"operator":[86,106],"given":[87],"product.":[91],"Specifically,":[92],"performance":[97],"for":[98],"systems":[101],"equal":[103],"induced":[107],"norm":[108],"this":[110,116],"operator.":[111],"results":[113],"obtained":[114],"bridge":[118],"gap":[120],"between":[121],"theory":[123,127],"metric":[126]},"counts_by_year":[{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}