{"id":"https://openalex.org/W2535870504","doi":"https://doi.org/10.1145/3049797.3049818","title":"Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms","display_name":"Forward Stochastic Reachability Analysis for Uncontrolled Linear Systems using Fourier Transforms","publication_year":2017,"publication_date":"2017-04-13","ids":{"openalex":"https://openalex.org/W2535870504","doi":"https://doi.org/10.1145/3049797.3049818","mag":"2535870504"},"language":"en","primary_location":{"id":"doi:10.1145/3049797.3049818","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3049797.3049818","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1610.04550","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050718717","display_name":"Abraham P. Vinod","orcid":"https://orcid.org/0000-0002-7955-9629"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Abraham P. Vinod","raw_affiliation_strings":["University of New Mexico, Albuquerque, NM, USA"],"affiliations":[{"raw_affiliation_string":"University of New Mexico, Albuquerque, NM, USA","institution_ids":["https://openalex.org/I169521973"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001678333","display_name":"Baisravan HomChaudhuri","orcid":"https://orcid.org/0000-0001-6121-4000"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Baisravan HomChaudhuri","raw_affiliation_strings":["University of New Mexico, Albuquerque, NM, USA"],"affiliations":[{"raw_affiliation_string":"University of New Mexico, Albuquerque, NM, USA","institution_ids":["https://openalex.org/I169521973"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5070060161","display_name":"Meeko Oishi","orcid":"https://orcid.org/0000-0003-3722-8837"},"institutions":[{"id":"https://openalex.org/I169521973","display_name":"University of New Mexico","ror":"https://ror.org/05fs6jp91","country_code":"US","type":"education","lineage":["https://openalex.org/I169521973"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Meeko M.K. Oishi","raw_affiliation_strings":["University of New Mexico, Albuquerque, NM, USA"],"affiliations":[{"raw_affiliation_string":"University of New Mexico, Albuquerque, NM, USA","institution_ids":["https://openalex.org/I169521973"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050718717"],"corresponding_institution_ids":["https://openalex.org/I169521973"],"apc_list":null,"apc_paid":null,"fwci":6.5561,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.97132221,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":91,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"35","last_page":"44"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9966999888420105,"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":0.9966999888420105,"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/T12158","display_name":"Guidance and Control Systems","score":0.9937000274658203,"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"}},{"id":"https://openalex.org/T13371","display_name":"Military Defense Systems Analysis","score":0.9868000149726868,"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/reachability","display_name":"Reachability","score":0.7233186364173889},{"id":"https://openalex.org/keywords/convexity","display_name":"Convexity","score":0.6838654279708862},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5519992113113403},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.5518421530723572},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5154610276222229},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.480114221572876},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.46423807740211487},{"id":"https://openalex.org/keywords/continuous-time-stochastic-process","display_name":"Continuous-time stochastic process","score":0.4506698250770569},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.44943299889564514},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.44337189197540283},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4375115633010864},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35574737191200256},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3222878575325012},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28611332178115845},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.23641258478164673},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08123365044593811}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.7233186364173889},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.6838654279708862},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5519992113113403},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.5518421530723572},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5154610276222229},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.480114221572876},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.46423807740211487},{"id":"https://openalex.org/C158535547","wikidata":"https://www.wikidata.org/wiki/Q5165437","display_name":"Continuous-time stochastic process","level":3,"score":0.4506698250770569},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.44943299889564514},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.44337189197540283},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4375115633010864},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35574737191200256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3222878575325012},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28611332178115845},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.23641258478164673},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08123365044593811},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1145/3049797.3049818","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3049797.3049818","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 20th International Conference on Hybrid Systems: Computation and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1610.04550","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.04550","pdf_url":"https://arxiv.org/pdf/1610.04550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1610.04550","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1610.04550","pdf_url":"https://arxiv.org/pdf/1610.04550","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3517431110","display_name":null,"funder_award_id":"CNS-1329878","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3582780070","display_name":null,"funder_award_id":"CMMI- 1254990","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6068018176","display_name":null,"funder_award_id":"IIS-1528047","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W234899517","https://openalex.org/W1489501223","https://openalex.org/W1494154421","https://openalex.org/W1521930086","https://openalex.org/W1524886571","https://openalex.org/W1559907478","https://openalex.org/W1569692898","https://openalex.org/W1584270973","https://openalex.org/W1824914642","https://openalex.org/W1964345118","https://openalex.org/W1988837127","https://openalex.org/W2007032806","https://openalex.org/W2012811607","https://openalex.org/W2015673634","https://openalex.org/W2023775503","https://openalex.org/W2025629731","https://openalex.org/W2044372633","https://openalex.org/W2047121664","https://openalex.org/W2056099894","https://openalex.org/W2060365990","https://openalex.org/W2075621462","https://openalex.org/W2080813827","https://openalex.org/W2084772009","https://openalex.org/W2087421501","https://openalex.org/W2098846072","https://openalex.org/W2099354898","https://openalex.org/W2105518356","https://openalex.org/W2105672294","https://openalex.org/W2109569369","https://openalex.org/W2123357397","https://openalex.org/W2126749600","https://openalex.org/W2148948872","https://openalex.org/W2296319761","https://openalex.org/W2400318990","https://openalex.org/W2414860269","https://openalex.org/W2524449277","https://openalex.org/W2581145181","https://openalex.org/W2584419649","https://openalex.org/W2963709688","https://openalex.org/W3004157836","https://openalex.org/W4240386814","https://openalex.org/W4250589301","https://openalex.org/W4255789359","https://openalex.org/W6631151876"],"related_works":["https://openalex.org/W2965246392","https://openalex.org/W129738973","https://openalex.org/W2888652631","https://openalex.org/W4200373676","https://openalex.org/W3020818737","https://openalex.org/W2912388972","https://openalex.org/W4238487991","https://openalex.org/W2042280983","https://openalex.org/W1997769777","https://openalex.org/W4237354330"],"abstract_inverted_index":{"We":[0,50],"propose":[1],"a":[2,71,76],"scalable":[3],"method":[4,18,39,84,95],"for":[5,10,100],"forward":[6,26,34,58],"stochastic":[7,27,35,59],"reachability":[8],"analysis":[9],"uncontrolled":[11],"linear":[12],"systems":[13,43],"with":[14,44],"affine":[15],"disturbance.":[16],"Our":[17],"uses":[19],"Fourier":[20],"transforms":[21],"to":[22,42,74],"efficiently":[23],"compute":[24],"the":[25,33,53,57,68,101],"reach":[28,36,60],"probability":[29,64,104],"measure":[30],"(density)":[31],"and":[32,62,103],"set.":[37],"This":[38],"is":[40],"applicable":[41],"bounded":[45],"or":[46],"unbounded":[47],"disturbance":[48],"sets.":[49],"also":[51],"examine":[52],"convexity":[54],"properties":[55],"of":[56,70,105],"set":[61],"its":[63],"density.":[65],"Motivated":[66],"by":[67],"problem":[69],"robot":[72],"attempting":[73],"capture":[75],"stochastically":[77],"moving,":[78],"non-adversarial":[79],"target,":[80],"we":[81],"demonstrate":[82],"our":[83,94],"on":[85],"two":[86],"simple":[87],"examples.":[88],"Where":[89],"traditional":[90],"approaches":[91],"provide":[92],"approximations,":[93],"provides":[96],"exact":[97],"analytical":[98],"expressions":[99],"densities":[102],"capture.":[106]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":5}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-10-28T00:00:00"}