{"id":"https://openalex.org/W2096839355","doi":"https://doi.org/10.1109/acc.2007.4282698","title":"Comparison Between SOS Approach and Slack Variable Approach for Non-negativity Check of Polynomial Functions: Single Variable Case","display_name":"Comparison Between SOS Approach and Slack Variable Approach for Non-negativity Check of Polynomial Functions: Single Variable Case","publication_year":2007,"publication_date":"2007-07-01","ids":{"openalex":"https://openalex.org/W2096839355","doi":"https://doi.org/10.1109/acc.2007.4282698","mag":"2096839355"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2007.4282698","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282698","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","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/A5043922434","display_name":"Masayuki Sato","orcid":"https://orcid.org/0000-0003-0387-3467"},"institutions":[{"id":"https://openalex.org/I2800865746","display_name":"Japan Aerospace Exploration Agency","ror":"https://ror.org/059yhyy33","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800865746"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Masayuki Sato","raw_affiliation_strings":["Japan Aerospace Exploration Agency, Institute of Space Technology and Aeronautics, Mitaka, Tokyo, Japan","Japan Aerosp. Exploration Agency, Tokyo"],"affiliations":[{"raw_affiliation_string":"Japan Aerospace Exploration Agency, Institute of Space Technology and Aeronautics, Mitaka, Tokyo, Japan","institution_ids":["https://openalex.org/I2800865746"]},{"raw_affiliation_string":"Japan Aerosp. Exploration Agency, Tokyo","institution_ids":["https://openalex.org/I2800865746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043595448","display_name":"Dimitri Peaucelle","orcid":"https://orcid.org/0000-0002-2640-2003"},"institutions":[{"id":"https://openalex.org/I2800865746","display_name":"Japan Aerospace Exploration Agency","ror":"https://ror.org/059yhyy33","country_code":"JP","type":"facility","lineage":["https://openalex.org/I2800865746"]},{"id":"https://openalex.org/I17866349","display_name":"Universit\u00e9 F\u00e9d\u00e9rale de Toulouse Midi-Pyr\u00e9n\u00e9es","ror":"https://ror.org/004raaa70","country_code":"FR","type":"education","lineage":["https://openalex.org/I17866349"]},{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I190497903","display_name":"Laboratoire d'Analyse et d'Architecture des Syst\u00e8mes","ror":"https://ror.org/03vcm6439","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I134560555","https://openalex.org/I190497903","https://openalex.org/I196454796","https://openalex.org/I205747304","https://openalex.org/I205747304","https://openalex.org/I4210095849","https://openalex.org/I4210159245","https://openalex.org/I4387153255","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862","https://openalex.org/I4405258862"]}],"countries":["FR","JP"],"is_corresponding":false,"raw_author_name":"Dimitri Peaucelle","raw_affiliation_strings":["LAAS-CNRS, University of Toulouse, France","Japan Aerosp. Exploration Agency, Tokyo"],"affiliations":[{"raw_affiliation_string":"LAAS-CNRS, University of Toulouse, France","institution_ids":["https://openalex.org/I17866349","https://openalex.org/I1294671590","https://openalex.org/I190497903"]},{"raw_affiliation_string":"Japan Aerosp. Exploration Agency, Tokyo","institution_ids":["https://openalex.org/I2800865746"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5043922434"],"corresponding_institution_ids":["https://openalex.org/I2800865746"],"apc_list":null,"apc_paid":null,"fwci":7.8384,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.97091627,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"6139","last_page":"6146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9983000159263611,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9983000159263611,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control Systems","score":0.993399977684021,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6892580389976501},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.6260779500007629},{"id":"https://openalex.org/keywords/negativity-effect","display_name":"Negativity effect","score":0.5155420303344727},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4658556580543518},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4403611421585083},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.36540207266807556},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33828824758529663},{"id":"https://openalex.org/keywords/psychology","display_name":"Psychology","score":0.129806250333786},{"id":"https://openalex.org/keywords/cognitive-psychology","display_name":"Cognitive psychology","score":0.1027289628982544},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10163372755050659}],"concepts":[{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6892580389976501},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.6260779500007629},{"id":"https://openalex.org/C7453019","wikidata":"https://www.wikidata.org/wiki/Q16254302","display_name":"Negativity effect","level":2,"score":0.5155420303344727},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4658556580543518},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4403611421585083},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.36540207266807556},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33828824758529663},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.129806250333786},{"id":"https://openalex.org/C180747234","wikidata":"https://www.wikidata.org/wiki/Q23373","display_name":"Cognitive psychology","level":1,"score":0.1027289628982544},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10163372755050659}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2007.4282698","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2007.4282698","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 American Control Conference","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7699999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W431400460","https://openalex.org/W1569149096","https://openalex.org/W1591868040","https://openalex.org/W1967184028","https://openalex.org/W1967344706","https://openalex.org/W1971443429","https://openalex.org/W1978065128","https://openalex.org/W2026578200","https://openalex.org/W2036031971","https://openalex.org/W2042421848","https://openalex.org/W2049087128","https://openalex.org/W2049225870","https://openalex.org/W2057000602","https://openalex.org/W2060602079","https://openalex.org/W2077088183","https://openalex.org/W2091288499","https://openalex.org/W2096839355","https://openalex.org/W2108489060","https://openalex.org/W2109815225","https://openalex.org/W2149845256","https://openalex.org/W2161507975","https://openalex.org/W2167219213","https://openalex.org/W2476606743","https://openalex.org/W2498847617","https://openalex.org/W3159909738","https://openalex.org/W6633987080","https://openalex.org/W6676560139"],"related_works":["https://openalex.org/W2140087070","https://openalex.org/W2001919142","https://openalex.org/W303980170","https://openalex.org/W2351491280","https://openalex.org/W2076063560","https://openalex.org/W2386767533","https://openalex.org/W1508761541","https://openalex.org/W3159909738","https://openalex.org/W246030616","https://openalex.org/W2096839355"],"abstract_inverted_index":{"This":[0],"note":[1],"addresses":[2],"the":[3,15,24,46,67,80],"comparison":[4],"between":[5],"Sums-Of-Squares":[6],"(SOS)":[7],"approach":[8,13,37,52,71,76,86],"and":[9,72],"Slack":[10],"Variable":[11],"(SV)":[12],"for":[14,79],"non-negativity":[16],"check":[17],"of":[18,35,40,50,55,93],"multiple":[19,41],"variable":[20],"polynomial":[21],"functions.":[22],"In":[23],"process":[25],"to":[26,97,105],"compare":[27],"these":[28],"methods,":[29],"we":[30],"derive":[31],"a":[32,56],"new":[33,74,84],"method":[34,49],"SV":[36,51,75,85],"with":[38,53,90],"use":[39,54],"slack":[42,58],"variables,":[43],"which":[44],"encompasses":[45],"previously":[47],"proposed":[48],"single":[57],"variable.":[59],"The":[60],"obtained":[61],"result":[62],"is":[63,87],"as":[64],"follows:":[65],"For":[66],"unbounded":[68],"case,":[69,82],"SOS":[70,98],"our":[73,83,107],"are":[77,103],"equivalent;":[78],"bounded":[81],"less":[88],"conservative":[89],"increased":[91],"number":[92],"decision":[94],"variables":[95],"compared":[96],"approach.":[99],"Several":[100],"numerical":[101],"examples":[102],"shown":[104],"illustrate":[106],"conclusions.":[108]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
