{"id":"https://openalex.org/W2087698734","doi":"https://doi.org/10.1109/tac.2014.2304399","title":"Optimal Stabilization Problem With Minimax Cost in a Critical Case","display_name":"Optimal Stabilization Problem With Minimax Cost in a Critical Case","publication_year":2014,"publication_date":"2014-02-12","ids":{"openalex":"https://openalex.org/W2087698734","doi":"https://doi.org/10.1109/tac.2014.2304399","mag":"2087698734"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2014.2304399","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2304399","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","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/A5039054938","display_name":"Victoria Grushkovskaya","orcid":"https://orcid.org/0000-0003-0439-6834"},"institutions":[{"id":"https://openalex.org/I4210089221","display_name":"Institute of Applied Mathematics and Mechanics","ror":"https://ror.org/006c77f48","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I4210089221"]},{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"funder","lineage":["https://openalex.org/I149851306"]}],"countries":["UA"],"is_corresponding":true,"raw_author_name":"Victoria Grushkovskaya","raw_affiliation_strings":["Institute of Applied Mathematicsand Mechanics, National Academy of Sciences ofUkraine, Donetsk, Ukraine"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematicsand Mechanics, National Academy of Sciences ofUkraine, Donetsk, Ukraine","institution_ids":["https://openalex.org/I4210089221","https://openalex.org/I149851306"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050131934","display_name":"Alexander Zuyev","orcid":"https://orcid.org/0000-0002-7610-5621"},"institutions":[{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"funder","lineage":["https://openalex.org/I149851306"]},{"id":"https://openalex.org/I4210089221","display_name":"Institute of Applied Mathematics and Mechanics","ror":"https://ror.org/006c77f48","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I4210089221"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Alexander Zuyev","raw_affiliation_strings":["Instituteof Applied Mathematics and Mechanics, NationalAcademy of Sciences of Ukraine, Donetsk, Ukraine"],"affiliations":[{"raw_affiliation_string":"Instituteof Applied Mathematics and Mechanics, NationalAcademy of Sciences of Ukraine, Donetsk, Ukraine","institution_ids":["https://openalex.org/I4210089221","https://openalex.org/I149851306"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039054938"],"corresponding_institution_ids":["https://openalex.org/I149851306","https://openalex.org/I4210089221"],"apc_list":null,"apc_paid":null,"fwci":0.8191,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.78937173,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"59","issue":"9","first_page":"2512","last_page":"2517"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9937000274658203,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9937000274658203,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9930999875068665,"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/T12158","display_name":"Guidance and Control Systems","score":0.9927999973297119,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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/minimax","display_name":"Minimax","score":0.8373285531997681},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6491408348083496},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6458173990249634},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6004279255867004},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.561402440071106},{"id":"https://openalex.org/keywords/maximization","display_name":"Maximization","score":0.5545654296875},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5340043306350708},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4804127514362335},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4785221815109253},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.43238401412963867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22617033123970032},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1740792989730835}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.8373285531997681},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6491408348083496},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6458173990249634},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6004279255867004},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.561402440071106},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.5545654296875},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5340043306350708},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4804127514362335},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4785221815109253},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.43238401412963867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22617033123970032},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1740792989730835},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2014.2304399","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2014.2304399","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W94233250","https://openalex.org/W1781243087","https://openalex.org/W1968468557","https://openalex.org/W1988942864","https://openalex.org/W2008995486","https://openalex.org/W2019562608","https://openalex.org/W2026246097","https://openalex.org/W2038150727","https://openalex.org/W2062692229","https://openalex.org/W2077730310","https://openalex.org/W2130104204","https://openalex.org/W2130417105","https://openalex.org/W2171972486","https://openalex.org/W2321052409","https://openalex.org/W2333223179","https://openalex.org/W2764109323","https://openalex.org/W4213264637","https://openalex.org/W4294967943","https://openalex.org/W6638233008"],"related_works":["https://openalex.org/W2016058626","https://openalex.org/W2474724840","https://openalex.org/W2895916002","https://openalex.org/W1814049089","https://openalex.org/W1977348009","https://openalex.org/W2369683208","https://openalex.org/W2084836983","https://openalex.org/W1530911128","https://openalex.org/W1555347637","https://openalex.org/W4309320703"],"abstract_inverted_index":{"This":[0,63],"work":[1],"addresses":[2],"the":[3,22,25,34,60,101],"optimal":[4,61,89],"stabilization":[5],"problem":[6,43],"of":[7,24,28,33,52,75,80,100],"a":[8,14,31,41,53,72,78,87,94],"nonlinear":[9,69],"control":[10],"system":[11,96],"by":[12],"using":[13],"smooth":[15],"output":[16],"feedback.":[17],"The":[18],"optimality":[19],"criterion":[20,39],"is":[21,56,66,91],"maximization":[23],"decay":[26],"rate":[27],"solutions":[29],"in":[30,71],"neighborhood":[32],"origin.":[35],"We":[36],"formulate":[37],"this":[38],"as":[40],"minimax":[42,88],"with":[44,77,97],"respect":[45],"to":[46,58],"non-integral":[47],"functional.":[48],"An":[49],"explicit":[50],"construction":[51],"Lyapunov":[54],"function":[55],"proposed":[57],"evaluate":[59],"cost.":[62],"design":[64],"methodology":[65],"justified":[67],"for":[68,93],"systems":[70],"critical":[73],"case":[74],"stability":[76],"pair":[79],"purely":[81],"imaginary":[82],"eigenvalues.":[83],"As":[84],"an":[85],"example,":[86],"controller":[90],"obtained":[92],"spring-pendulum":[95],"partial":[98],"measurements":[99],"state":[102],"vector.":[103]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}