{"id":"https://openalex.org/W2972591310","doi":"https://doi.org/10.23919/acc.2019.8814931","title":"A Sum of Squares Optimization Approach to Uncertainty Quantification","display_name":"A Sum of Squares Optimization Approach to Uncertainty Quantification","publication_year":2019,"publication_date":"2019-07-01","ids":{"openalex":"https://openalex.org/W2972591310","doi":"https://doi.org/10.23919/acc.2019.8814931","mag":"2972591310"},"language":"en","primary_location":{"id":"doi:10.23919/acc.2019.8814931","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2019.8814931","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 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/A5025576040","display_name":"Brendon K. Colbert","orcid":"https://orcid.org/0000-0003-1580-555X"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Brendon K. Colbert","raw_affiliation_strings":["Arizona State University, Tempe, AZ, 85287, USA","Arizona State University, Tempe, AZ, USA"],"affiliations":[{"raw_affiliation_string":"Arizona State University, Tempe, AZ, 85287, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112043830","display_name":"Luis G. Crespo","orcid":null},"institutions":[{"id":"https://openalex.org/I1319063186","display_name":"Langley Research Center","ror":"https://ror.org/0399mhs52","country_code":"US","type":"facility","lineage":["https://openalex.org/I1319063186","https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luis G. Crespo","raw_affiliation_strings":["NASA Langley Research Center, Hampton, VA, 23681, USA","NASA Langley Research Center, Hampton, VA, USA"],"affiliations":[{"raw_affiliation_string":"NASA Langley Research Center, Hampton, VA, 23681, USA","institution_ids":["https://openalex.org/I1319063186"]},{"raw_affiliation_string":"NASA Langley Research Center, Hampton, VA, USA","institution_ids":["https://openalex.org/I1319063186"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077552862","display_name":"Matthew M. Peet","orcid":"https://orcid.org/0000-0001-9360-6738"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Matthew M. Peet","raw_affiliation_strings":["Arizona State University, Tempe, AZ, 85287, USA","Arizona State University, Tempe, AZ, USA"],"affiliations":[{"raw_affiliation_string":"Arizona State University, Tempe, AZ, 85287, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Arizona State University, Tempe, AZ, USA","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5025576040"],"corresponding_institution_ids":["https://openalex.org/I55732556"],"apc_list":null,"apc_paid":null,"fwci":0.4838,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72091742,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"5378","last_page":"5384"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9997000098228455,"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":0.9854000210762024,"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/T11236","display_name":"Control Systems and Identification","score":0.9721999764442444,"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/computer-science","display_name":"Computer science","score":0.522634744644165},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.43586260080337524},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3282286524772644},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.25315719842910767},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.24944278597831726}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.522634744644165},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.43586260080337524},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3282286524772644},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25315719842910767},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.24944278597831726},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/acc.2019.8814931","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc.2019.8814931","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2019 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":7,"referenced_works":["https://openalex.org/W1516536271","https://openalex.org/W1877096495","https://openalex.org/W1964730816","https://openalex.org/W2054137409","https://openalex.org/W2155724501","https://openalex.org/W2579601083","https://openalex.org/W2972550732"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052","https://openalex.org/W4402327032","https://openalex.org/W2382290278"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,21,36,44,59,97,101,108],"Sum":[4],"of":[5,20,27,62,92,123],"Squares":[6],"(SOS)":[7],"optimization":[8],"technique":[9],"for":[10,48,146,164],"using":[11,35,107],"multivariate":[12],"data":[13,42],"to":[14,39,73,80,110],"estimate":[15],"the":[16,41,63,93,114,124,128],"probability":[17],"density":[18,66,130],"function":[19],"non-Gaussian":[22],"generating":[23],"process.":[24],"The":[25,70],"class":[26],"distributions":[28],"over":[29],"which":[30],"we":[31,135,150],"optimize,":[32],"result":[33],"from":[34],"polynomial":[37,60],"map":[38],"lift":[40],"into":[43,67],"higher-dimensional":[45],"space,":[46,55],"solving":[47],"an":[49],"optimal":[50,129],"Gaussian":[51],"fit":[52],"in":[53,132],"this":[54],"and":[56,84,105,171],"then":[57,100,136],"projecting":[58],"slice":[61],"resulting":[64,71],"joint":[65],"physical":[68],"space.":[69],"distribution,":[72],"be":[74,162],"called":[75],"Sliced":[76],"Normal,":[77],"is":[78],"able":[79],"characterize":[81],"multimodal":[82],"responses":[83],"strong":[85],"parameter":[86],"dependencies.":[87],"We":[88],"investigate":[89],"several":[90],"formulations":[91],"problem,":[94],"first":[95],"maximizing":[96],"log-likelihood":[98,103,116],"function,":[99,104],"worst-case":[102],"finally":[106],"heuristic":[109],"increase":[111],"sparsity":[112],"within":[113],"maximum":[115],"formulation":[117],"-":[118],"thereby":[119],"identifying":[120],"independent":[121],"subsets":[122],"random":[125],"variables.":[126],"Using":[127],"functions":[131],"each":[133],"scenario,":[134],"propose":[137],"semi-algebraic":[138],"sets":[139],"representing":[140],"confidence":[141],"regions,":[142],"or":[143],"\u201csafe":[144,155],"sets,\u201d":[145],"future":[147],"data.":[148],"Finally,":[149],"show":[151],"numerically":[152],"that":[153],"these":[154],"sets\u201d":[156],"are":[157],"reliable":[158],"and,":[159],"hence,":[160],"can":[161],"used":[163],"system":[165],"identification,":[166],"fault":[167],"detection,":[168],"robustness":[169],"analysis,":[170],"robust":[172],"control":[173],"design.":[174]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
