{"id":"https://openalex.org/W3120195637","doi":"https://doi.org/10.1109/tac.2021.3051000","title":"An Analytical Safe Approximation to Joint Chance-Constrained Programming With Additive Gaussian Noises","display_name":"An Analytical Safe Approximation to Joint Chance-Constrained Programming With Additive Gaussian Noises","publication_year":2021,"publication_date":"2021-01-13","ids":{"openalex":"https://openalex.org/W3120195637","doi":"https://doi.org/10.1109/tac.2021.3051000","mag":"3120195637"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2021.3051000","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3051000","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/A5100341015","display_name":"Nan Li","orcid":"https://orcid.org/0000-0001-7928-8796"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nan Li","raw_affiliation_strings":["Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":"https://orcid.org/0000-0001-7928-8796","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078022728","display_name":"Ilya Kolmanovsky","orcid":"https://orcid.org/0000-0002-7225-4160"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ilya Kolmanovsky","raw_affiliation_strings":["Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":"https://orcid.org/0000-0002-7225-4160","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074685221","display_name":"Anouck Girard","orcid":"https://orcid.org/0000-0003-3410-7271"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anouck Girard","raw_affiliation_strings":["Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA"],"raw_orcid":"https://orcid.org/0000-0003-3410-7271","affiliations":[{"raw_affiliation_string":"Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, USA","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":0.7914,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.71896852,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"66","issue":"11","first_page":"5490","last_page":"5497"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11413","display_name":"Risk and Portfolio Optimization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/T11413","display_name":"Risk and Portfolio Optimization","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"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/T10969","display_name":"Water resources management and optimization","score":0.996399998664856,"subfield":{"id":"https://openalex.org/subfields/2212","display_name":"Ocean 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/T12709","display_name":"Optimization and Mathematical Programming","score":0.9957000017166138,"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/mathematical-optimization","display_name":"Mathematical optimization","score":0.5803868770599365},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.5538281202316284},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5028521418571472},{"id":"https://openalex.org/keywords/linear-approximation","display_name":"Linear approximation","score":0.4863465428352356},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.481190025806427},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.4711322486400604},{"id":"https://openalex.org/keywords/stochastic-approximation","display_name":"Stochastic approximation","score":0.4496029019355774},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4313586950302124},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.41511163115501404},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.391693115234375},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36651068925857544},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08247768878936768}],"concepts":[{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5803868770599365},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.5538281202316284},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5028521418571472},{"id":"https://openalex.org/C160824197","wikidata":"https://www.wikidata.org/wiki/Q2071054","display_name":"Linear approximation","level":3,"score":0.4863465428352356},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.481190025806427},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.4711322486400604},{"id":"https://openalex.org/C55479107","wikidata":"https://www.wikidata.org/wiki/Q97663916","display_name":"Stochastic approximation","level":3,"score":0.4496029019355774},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4313586950302124},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.41511163115501404},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.391693115234375},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36651068925857544},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08247768878936768},{"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/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2021.3051000","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2021.3051000","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":[{"score":0.47999998927116394,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G4079282771","display_name":null,"funder_award_id":"CNS 1544844","funder_id":"https://openalex.org/F4320309085","funder_display_name":"Center for Selective C-H Functionalization, National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320309085","display_name":"Center for Selective C-H Functionalization, National Science Foundation","ror":"https://ror.org/02h8v7m77"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W66371144","https://openalex.org/W1553372930","https://openalex.org/W1647779468","https://openalex.org/W1963497305","https://openalex.org/W2003777645","https://openalex.org/W2008618334","https://openalex.org/W2028628423","https://openalex.org/W2034732300","https://openalex.org/W2038765090","https://openalex.org/W2060416080","https://openalex.org/W2062843008","https://openalex.org/W2067778155","https://openalex.org/W2083350518","https://openalex.org/W2086691890","https://openalex.org/W2094435766","https://openalex.org/W2097148013","https://openalex.org/W2099506495","https://openalex.org/W2101496914","https://openalex.org/W2117781171","https://openalex.org/W2132670515","https://openalex.org/W2139869783","https://openalex.org/W2143514150","https://openalex.org/W2149945166","https://openalex.org/W2164499670","https://openalex.org/W2296319761","https://openalex.org/W2557055507","https://openalex.org/W2738294177","https://openalex.org/W2750408863","https://openalex.org/W2903687130","https://openalex.org/W2945278523","https://openalex.org/W2965322768","https://openalex.org/W2966850587","https://openalex.org/W3102247235","https://openalex.org/W4250589301","https://openalex.org/W4250913065","https://openalex.org/W4295094175"],"related_works":["https://openalex.org/W2134007003","https://openalex.org/W2019875157","https://openalex.org/W3122413977","https://openalex.org/W4310831616","https://openalex.org/W2165420145","https://openalex.org/W1859974437","https://openalex.org/W189995875","https://openalex.org/W4388667053","https://openalex.org/W4231428347","https://openalex.org/W3177870706"],"abstract_inverted_index":{"We":[0,46],"propose":[1],"a":[2,17,42,67,91],"safe":[3,50,55,88],"approximation":[4,22,40,51,56,89],"to":[5,52,66,97],"joint":[6,58],"chance-constrained":[7,59],"programming,":[8],"where":[9],"the":[10,39,75],"constraint":[11],"functions":[12],"are":[13],"additively":[14],"dependent":[15],"on":[16,62],"normally-distributed":[18],"random":[19],"vector.":[20],"The":[21],"is":[23,41,83],"analytical,":[24],"meaning":[25],"that":[26,85],"it":[27],"requires":[28],"neither":[29],"numerical":[30,72],"integrations":[31],"nor":[32],"sampling-based":[33],"probability":[34],"approximations.":[35],"Under":[36],"mild":[37],"assumptions,":[38],"standard":[43],"nonlinear":[44],"program.":[45],"compare":[47],"this":[48],"new":[49],"another":[53],"analytical":[54],"for":[57],"programming":[60],"based":[61],"Boole's":[63],"inequality":[64],"and":[65],"scenario":[68],"approach":[69],"through":[70],"two":[71,99],"examples":[73],"representing":[74],"constrained":[76],"control":[77],"of":[78,94],"linear":[79],"Gauss\u2013Markov":[80],"models.":[81],"It":[82],"shown":[84],"our":[86],"proposed":[87],"has":[90],"lower":[92],"degree":[93],"conservativeness":[95],"compared":[96],"these":[98],"alternative":[100],"approaches.":[101]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-12T21:12:35.861297","created_date":"2025-10-10T00:00:00"}
