{"id":"https://openalex.org/W2571545337","doi":"https://doi.org/10.1109/cdc.2016.7798890","title":"Convex estimation of the \u03b1-confidence reachable set for systems with parametric uncertainty","display_name":"Convex estimation of the \u03b1-confidence reachable set for systems with parametric uncertainty","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2571545337","doi":"https://doi.org/10.1109/cdc.2016.7798890","mag":"2571545337"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2016.7798890","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798890","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","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/A5048486449","display_name":"Patrick Holmes","orcid":"https://orcid.org/0000-0001-5252-4664"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Patrick Holmes","raw_affiliation_strings":["Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019247599","display_name":"Shreyas Kousik","orcid":"https://orcid.org/0000-0003-1348-7463"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shreyas Kousik","raw_affiliation_strings":["Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081141984","display_name":"Shankar Mohan","orcid":"https://orcid.org/0000-0002-6107-7672"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shankar Mohan","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI","institution_ids":["https://openalex.org/I27837315"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053632225","display_name":"Ram Vasudevan","orcid":"https://orcid.org/0000-0003-1978-0572"},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan\u2013Ann Arbor","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ram Vasudevan","raw_affiliation_strings":["Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI","institution_ids":["https://openalex.org/I27837315"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5048486449"],"corresponding_institution_ids":["https://openalex.org/I27837315"],"apc_list":null,"apc_paid":null,"fwci":0.9125,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.76468138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"4097","last_page":"4103"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9932000041007996,"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"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9932000041007996,"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"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9921000003814697,"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/T10142","display_name":"Formal Methods in Verification","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.7964134216308594},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.6234151124954224},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.600672721862793},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.564701497554779},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.537140965461731},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5256056785583496},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5164518356323242},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4819212257862091},{"id":"https://openalex.org/keywords/sensitivity-analysis","display_name":"Sensitivity analysis","score":0.4701409935951233},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.445239782333374},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.4197666645050049},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37412434816360474},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35924649238586426},{"id":"https://openalex.org/keywords/uncertainty-analysis","display_name":"Uncertainty analysis","score":0.3578457832336426},{"id":"https://openalex.org/keywords/simulation","display_name":"Simulation","score":0.08303454518318176}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.7964134216308594},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.6234151124954224},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.600672721862793},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.564701497554779},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.537140965461731},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5256056785583496},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5164518356323242},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4819212257862091},{"id":"https://openalex.org/C176147448","wikidata":"https://www.wikidata.org/wiki/Q1889114","display_name":"Sensitivity analysis","level":3,"score":0.4701409935951233},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.445239782333374},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.4197666645050049},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37412434816360474},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35924649238586426},{"id":"https://openalex.org/C177803969","wikidata":"https://www.wikidata.org/wiki/Q29205","display_name":"Uncertainty analysis","level":2,"score":0.3578457832336426},{"id":"https://openalex.org/C44154836","wikidata":"https://www.wikidata.org/wiki/Q45045","display_name":"Simulation","level":1,"score":0.08303454518318176},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2016.7798890","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798890","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.75,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W564963347","https://openalex.org/W1914309457","https://openalex.org/W1967344706","https://openalex.org/W1992402930","https://openalex.org/W2030070978","https://openalex.org/W2033118636","https://openalex.org/W2045814149","https://openalex.org/W2050383062","https://openalex.org/W2057789475","https://openalex.org/W2085744412","https://openalex.org/W2093350522","https://openalex.org/W2116364955","https://openalex.org/W2130005755","https://openalex.org/W2133404041","https://openalex.org/W2167710281","https://openalex.org/W2313274380","https://openalex.org/W2964320632","https://openalex.org/W4214520334","https://openalex.org/W4293203252"],"related_works":["https://openalex.org/W4249135812","https://openalex.org/W2116089868","https://openalex.org/W93577605","https://openalex.org/W2033170585","https://openalex.org/W1991803138","https://openalex.org/W337241763","https://openalex.org/W1983007452","https://openalex.org/W4387046439","https://openalex.org/W3128892391","https://openalex.org/W2115703496"],"abstract_inverted_index":{"Accurately":[0],"modeling":[1],"and":[2],"verifying":[3],"the":[4,20,26,32,41,56,82,97,106,113,120,141,169,179],"correct":[5],"operation":[6],"of":[7,58,60,84,96,104,115,122,124,156,160,171,177,189],"systems":[8,100,196],"interacting":[9],"in":[10,81],"dynamic":[11],"environments":[12],"is":[13,148,162,192],"challenging.":[14],"By":[15],"leveraging":[16],"parametric":[17,77,129,198],"uncertainty":[18,85,130],"within":[19],"model":[21],"description,":[22],"one":[23,36],"can":[24,86],"relax":[25],"requirement":[27],"to":[28,54,68,88,118,164,168],"describe":[29,119],"interactions":[30],"with":[31,128,140,150,197],"environment":[33],"exactly;":[34],"however,":[35],"must":[37],"still":[38],"guarantee":[39],"that":[40,65,101,174],"model,":[42],"despite":[43,76,185],"uncertainty,":[44],"behaves":[45],"acceptably.":[46],"This":[47,145],"paper":[48,92],"presents":[49],"a":[50,61,71,125,132,154],"convex":[51],"optimization":[52],"method":[53,191],"compute":[55,165],"set":[57,75,170,183],"configurations":[59],"polynomial":[62],"dynamical":[63],"system":[64,127],"are":[66,102,175],"able":[67],"safely":[69,184],"reach":[70],"user":[72,180],"defined":[73,181],"target":[74,182],"uncertainty.":[78,186,199],"Since":[79],"planning":[80],"presence":[83],"lead":[87],"undesirable":[89],"conservativeness,":[90],"this":[91,190],"computes":[93],"those":[94],"trajectories":[95,123,142],"uncertain":[98],"nonlinear":[99,126],"\u03b1-probable":[103,176],"reaching":[105,178],"desired":[107],"configuration.":[108],"The":[109,187],"presented":[110],"approach":[111],"uses":[112],"notion":[114],"occupation":[116],"measures":[117,136],"evolution":[121],"as":[131],"linear":[133,146],"equation":[134,147],"over":[135],"whose":[137],"supports":[138],"coincide":[139],"under":[143],"investigation.":[144],"approximated":[149],"vanishing":[151],"conservatism":[152],"using":[153],"hierarchy":[155],"semidefinite":[157],"programs":[158],"each":[159],"which":[161],"proven":[163],"an":[166],"approximation":[167],"initial":[172],"conditions":[173],"efficacy":[188],"illustrated":[193],"on":[194],"three":[195]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}