{"id":"https://openalex.org/W2043766205","doi":"https://doi.org/10.1137/130941195","title":"Two Equivalence Theorems of Different Kinds of Optimal Control Problems for Schr\u00f6dinger Equations","display_name":"Two Equivalence Theorems of Different Kinds of Optimal Control Problems for Schr\u00f6dinger Equations","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2043766205","doi":"https://doi.org/10.1137/130941195","mag":"2043766205"},"language":"en","primary_location":{"id":"doi:10.1137/130941195","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130941195","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-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/A5076622154","display_name":"Yubiao Zhang","orcid":"https://orcid.org/0000-0002-3843-3384"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yubiao Zhang","raw_affiliation_strings":["School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5076622154"],"corresponding_institution_ids":["https://openalex.org/I37461747"],"apc_list":null,"apc_paid":null,"fwci":1.683,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.85763012,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"53","issue":"2","first_page":"926","last_page":"947"},"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":0.9998999834060669,"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":0.9998999834060669,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9987999796867371,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9667999744415283,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8639832735061646},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.8237453103065491},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.7274155020713806},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.6051584482192993},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45972415804862976},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3785340189933777},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2827906012535095}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8639832735061646},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.8237453103065491},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.7274155020713806},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.6051584482192993},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45972415804862976},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3785340189933777},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2827906012535095},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/130941195","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130941195","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W629793771","https://openalex.org/W1965657934","https://openalex.org/W1978535908","https://openalex.org/W1990990142","https://openalex.org/W1991288696","https://openalex.org/W1993046097","https://openalex.org/W1995647377","https://openalex.org/W1996065896","https://openalex.org/W2009404181","https://openalex.org/W2011790132","https://openalex.org/W2012395674","https://openalex.org/W2031521898","https://openalex.org/W2043909370","https://openalex.org/W2053944345","https://openalex.org/W2067590872","https://openalex.org/W2068257048","https://openalex.org/W2078970956","https://openalex.org/W2081158290","https://openalex.org/W2116715073","https://openalex.org/W2149102153","https://openalex.org/W2323501086","https://openalex.org/W2963607086"],"related_works":["https://openalex.org/W1892002403","https://openalex.org/W4287830728","https://openalex.org/W4309005041","https://openalex.org/W2962746246","https://openalex.org/W3097860111","https://openalex.org/W3123455607","https://openalex.org/W1989531755","https://openalex.org/W2138137818","https://openalex.org/W1967384683","https://openalex.org/W2460944165"],"abstract_inverted_index":{"This":[0],"paper":[1],"builds":[2],"up":[3],"two":[4],"equivalence":[5,24,67],"theorems":[6],"for":[7],"different":[8],"kinds":[9],"of":[10,14,25,42,57,68,85],"optimal":[11,58,70,73,77,86],"control":[12,33,49,60,71,75,79,88],"problems":[13,34,50],"internally":[15],"controlled":[16],"Schr\u00f6dinger":[17],"equations.":[18],"The":[19,62],"first":[20,55],"one":[21,64],"is":[22,65],"an":[23,66],"the":[26,30,36,40,43,54,82],"minimal":[27,31,47],"norm":[28,78],"and":[29,81],"time":[32,48,59,87],"where":[35],"target":[37,74],"sets":[38],"are":[39,51],"origin":[41],"state":[44],"space.":[45],"(The":[46],"also":[52],"called":[53],"type":[56,84],"problems.)":[61],"second":[63,83],"three":[69],"problems:":[72],"problems,":[76,80],"problems.":[89]},"counts_by_year":[{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}