{"id":"https://openalex.org/W1550613469","doi":"https://doi.org/10.23919/ecc.2009.7074473","title":"Safety assessment for stochastic linear systems using enclosing hulls of probability density functions","display_name":"Safety assessment for stochastic linear systems using enclosing hulls of probability density functions","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W1550613469","doi":"https://doi.org/10.23919/ecc.2009.7074473","mag":"1550613469"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2009.7074473","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2009.7074473","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 European Control Conference (ECC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://mediatum.ub.tum.de/1289123","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5005383495","display_name":"Matthias Althoff","orcid":"https://orcid.org/0000-0003-3733-842X"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Matthias Althoff","raw_affiliation_strings":["Institute of Automatic Control Engineering (LSR), Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany","[Institute of Automatic Control Engineering (LSR), Technische Universit\u00e4t M\u00fcnchen, 80290, Germany]"],"affiliations":[{"raw_affiliation_string":"Institute of Automatic Control Engineering (LSR), Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"[Institute of Automatic Control Engineering (LSR), Technische Universit\u00e4t M\u00fcnchen, 80290, Germany]","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040756775","display_name":"Olaf Stursberg","orcid":"https://orcid.org/0000-0002-9600-457X"},"institutions":[{"id":"https://openalex.org/I106157433","display_name":"University of Kassel","ror":"https://ror.org/04zc7p361","country_code":"DE","type":"education","lineage":["https://openalex.org/I106157433"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Olaf Stursberg","raw_affiliation_strings":["Dept. of Electrical Eng., University of Kassel, Germany","Institute of Control and System Theory, Dept. of Electrical Engineering, University of Kassel (Germany)"],"affiliations":[{"raw_affiliation_string":"Dept. of Electrical Eng., University of Kassel, Germany","institution_ids":["https://openalex.org/I106157433"]},{"raw_affiliation_string":"Institute of Control and System Theory, Dept. of Electrical Engineering, University of Kassel (Germany)","institution_ids":["https://openalex.org/I106157433"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081223790","display_name":"Martin Buss","orcid":"https://orcid.org/0000-0002-1776-2752"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Buss","raw_affiliation_strings":["Institute of Automatic Control Engineering (LSR), Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany","[Institute of Automatic Control Engineering (LSR), Technische Universit\u00e4t M\u00fcnchen, 80290, Germany]"],"affiliations":[{"raw_affiliation_string":"Institute of Automatic Control Engineering (LSR), Technische Universit\u00e4t M\u00fcnchen, M\u00fcnchen, Germany","institution_ids":["https://openalex.org/I62916508"]},{"raw_affiliation_string":"[Institute of Automatic Control Engineering (LSR), Technische Universit\u00e4t M\u00fcnchen, 80290, Germany]","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5005383495"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":0.7698,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.75104279,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"625","last_page":"630"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10876","display_name":"Fault Detection and Control 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/T10876","display_name":"Fault Detection and Control 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/T11236","display_name":"Control Systems and Identification","score":0.9872999787330627,"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/probability-density-function","display_name":"Probability density function","score":0.7986838817596436},{"id":"https://openalex.org/keywords/white-noise","display_name":"White noise","score":0.6779214143753052},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6292765736579895},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.5400204658508301},{"id":"https://openalex.org/keywords/additive-white-gaussian-noise","display_name":"Additive white Gaussian noise","score":0.520304262638092},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5102450847625732},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.49939966201782227},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.49187207221984863},{"id":"https://openalex.org/keywords/gaussian-noise","display_name":"Gaussian noise","score":0.47771263122558594},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.469779908657074},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.45160165429115295},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4351632297039032},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4292597472667694},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4244050085544586},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36614564061164856},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3098282814025879},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.22577962279319763},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21542730927467346},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10729017853736877}],"concepts":[{"id":"https://openalex.org/C197055811","wikidata":"https://www.wikidata.org/wiki/Q207522","display_name":"Probability density function","level":2,"score":0.7986838817596436},{"id":"https://openalex.org/C112633086","wikidata":"https://www.wikidata.org/wiki/Q381287","display_name":"White noise","level":2,"score":0.6779214143753052},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6292765736579895},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.5400204658508301},{"id":"https://openalex.org/C169334058","wikidata":"https://www.wikidata.org/wiki/Q353292","display_name":"Additive white Gaussian noise","level":3,"score":0.520304262638092},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5102450847625732},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.49939966201782227},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.49187207221984863},{"id":"https://openalex.org/C4199805","wikidata":"https://www.wikidata.org/wiki/Q2725903","display_name":"Gaussian noise","level":2,"score":0.47771263122558594},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.469779908657074},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.45160165429115295},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4351632297039032},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4292597472667694},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4244050085544586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36614564061164856},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3098282814025879},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.22577962279319763},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21542730927467346},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10729017853736877},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23919/ecc.2009.7074473","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2009.7074473","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 European Control Conference (ECC)","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.149.2094","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.149.2094","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lsr.ei.tum.de/fileadmin/publications/M._Althoff/AlthoffStursbergBuss_ECC09.pdf","raw_type":"text"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1289123","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1289123","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"ConferencePaper"},{"id":"pmh:oai:mediatum.ub.tum.de:node/979636","is_oa":false,"landing_page_url":"https://mediatum.ub.tum.de/979636","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:mediatum.ub.tum.de:node/1289123","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1289123","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"ConferencePaper"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4399999976158142}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W132789959","https://openalex.org/W309294495","https://openalex.org/W1484033701","https://openalex.org/W1569692898","https://openalex.org/W1598511836","https://openalex.org/W1726255445","https://openalex.org/W1824914642","https://openalex.org/W1997398211","https://openalex.org/W2016309114","https://openalex.org/W2033118636","https://openalex.org/W2099698956","https://openalex.org/W2131441094","https://openalex.org/W2135128809","https://openalex.org/W2145201569","https://openalex.org/W2527557516","https://openalex.org/W2999431506","https://openalex.org/W3020882730","https://openalex.org/W4233358567","https://openalex.org/W4234011924"],"related_works":["https://openalex.org/W1974392290","https://openalex.org/W1911817635","https://openalex.org/W2810224748","https://openalex.org/W2747300875","https://openalex.org/W2353656796","https://openalex.org/W2011915004","https://openalex.org/W2130974430","https://openalex.org/W3103566292","https://openalex.org/W2074565401","https://openalex.org/W1607924090"],"abstract_inverted_index":{"This":[0,69],"contribution":[1],"addresses":[2],"the":[3,7,21,41,49,86],"problem":[4],"of":[5,26,40],"computing":[6],"probability":[8,25,42],"that":[9,88],"a":[10],"linear":[11],"system":[12],"with":[13,48],"uncertain":[14,65],"inputs":[15],"reaches":[16],"an":[17,33,77],"unsafe":[18,28,51],"region":[19],"in":[20,76,85],"state":[22],"space.":[23],"The":[24,80],"reaching":[27],"states":[29],"is":[30,62,83],"bounded":[31],"by":[32,36],"upper":[34],"limit,":[35],"intersecting":[37],"enclosing":[38],"hulls":[39],"density":[43],"function":[44],"for":[45],"time":[46],"intervals":[47],"specified":[50,67],"regions.":[52],"Disturbances":[53],"are":[54],"modeled":[55,63],"as":[56,64],"white":[57,73],"Gaussian":[58],"noise,":[59],"whose":[60],"mean":[61],"within":[66],"sets.":[68],"allows":[70],"to":[71],"consider":[72],"non-Gaussian":[74],"noise":[75],"over-approximative":[78],"manner.":[79],"presented":[81],"approach":[82],"efficient":[84],"sense":[87],"high-dimensional":[89],"systems":[90],"can":[91],"be":[92],"handled.":[93]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}