{"id":"https://openalex.org/W2116439388","doi":"https://doi.org/10.1109/acc.2009.5160680","title":"Computation of uncertainty distributions in complex dynamical systems","display_name":"Computation of uncertainty distributions in complex dynamical systems","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2116439388","doi":"https://doi.org/10.1109/acc.2009.5160680","mag":"2116439388"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2009.5160680","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2009.5160680","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 American Control Conference","raw_type":"proceedings-article"},"type":"conference-paper","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/A5062361928","display_name":"Thordur Runolfsson","orcid":null},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Thordur Runolfsson","raw_affiliation_strings":["School of Electrical and Computer Engineering, University of Oklahama, Norman, OK, USA","School of Electrical and Computer Engineering, The University of Oklahoma, Norman, 73019 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, University of Oklahama, Norman, OK, USA","institution_ids":["https://openalex.org/I8692664"]},{"raw_affiliation_string":"School of Electrical and Computer Engineering, The University of Oklahoma, Norman, 73019 USA","institution_ids":["https://openalex.org/I8692664"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111628967","display_name":"Chenxi Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chenxi Lin","raw_affiliation_strings":["School of Electrical and Computer Engineering, University of Oklahama, Norman, OK, USA","School of Electrical and Computer Engineering, The University of Oklahoma, Norman, 73019 USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, University of Oklahama, Norman, OK, USA","institution_ids":["https://openalex.org/I8692664"]},{"raw_affiliation_string":"School of Electrical and Computer Engineering, The University of Oklahoma, Norman, 73019 USA","institution_ids":["https://openalex.org/I8692664"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I8692664"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"29","issue":null,"first_page":"2458","last_page":"2463"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9994000196456909,"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":0.9994000196456909,"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/T12056","display_name":"Markov Chains and Monte Carlo Methods","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11236","display_name":"Control Systems and Identification","score":0.9376999735832214,"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/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.6531668901443481},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.632218062877655},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5371772646903992},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.5080709457397461},{"id":"https://openalex.org/keywords/state-space","display_name":"State space","score":0.4922422468662262},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49191761016845703},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.47468993067741394},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47376635670661926},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.4480840265750885},{"id":"https://openalex.org/keywords/linear-dynamical-system","display_name":"Linear dynamical system","score":0.43559786677360535},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4353174865245819},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.43371421098709106},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4308268129825592},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4256453514099121},{"id":"https://openalex.org/keywords/invariant-measure","display_name":"Invariant measure","score":0.41130274534225464},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.37392204999923706},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.30740654468536377},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.24341511726379395},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14614921808242798}],"concepts":[{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.6531668901443481},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.632218062877655},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5371772646903992},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.5080709457397461},{"id":"https://openalex.org/C72434380","wikidata":"https://www.wikidata.org/wiki/Q230930","display_name":"State space","level":2,"score":0.4922422468662262},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49191761016845703},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.47468993067741394},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47376635670661926},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.4480840265750885},{"id":"https://openalex.org/C114275822","wikidata":"https://www.wikidata.org/wiki/Q621512","display_name":"Linear dynamical system","level":3,"score":0.43559786677360535},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4353174865245819},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.43371421098709106},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4308268129825592},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4256453514099121},{"id":"https://openalex.org/C115667082","wikidata":"https://www.wikidata.org/wiki/Q4200518","display_name":"Invariant measure","level":3,"score":0.41130274534225464},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.37392204999923706},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.30740654468536377},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.24341511726379395},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14614921808242798},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C122044880","wikidata":"https://www.wikidata.org/wiki/Q5498822","display_name":"Ergodic theory","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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":1,"locations":[{"id":"doi:10.1109/acc.2009.5160680","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2009.5160680","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2009 American Control Conference","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":13,"referenced_works":["https://openalex.org/W1506169651","https://openalex.org/W1802196594","https://openalex.org/W2001537639","https://openalex.org/W2011712695","https://openalex.org/W2031716212","https://openalex.org/W2065389195","https://openalex.org/W2074388175","https://openalex.org/W2091491115","https://openalex.org/W2768524679","https://openalex.org/W4205394018","https://openalex.org/W4232499108","https://openalex.org/W4292366057","https://openalex.org/W6658461243"],"related_works":["https://openalex.org/W2230606337","https://openalex.org/W4250831671","https://openalex.org/W2592826714","https://openalex.org/W4238935091","https://openalex.org/W2050811761","https://openalex.org/W2952544653","https://openalex.org/W2738494313","https://openalex.org/W2044696633","https://openalex.org/W2051295858","https://openalex.org/W1587625526"],"abstract_inverted_index":{"The":[0,100,128],"computation":[1],"of":[2,6,18,23,40,68,79,83,96],"the":[3,19,24,66,77,80,84,88,97,112],"stationary":[4,98],"distribution":[5],"an":[7,13,61,118],"uncertain":[8],"nonlinear":[9],"dynamical":[10,89],"system":[11],"is":[12,29,103,126,130],"important":[14],"tool":[15],"in":[16],"analysis":[17],"long":[20],"term":[21],"behavior":[22],"system.":[25,136],"One":[26],"common":[27],"approach":[28,63,129],"to":[30,46,72,105],"use":[31],"a":[32,48,93,107,133],"Monte":[33],"Carlo":[34],"type":[35,39],"method.":[36],"However,":[37],"that":[38],"method":[41],"requires":[42],"many":[43],"simulations":[44],"runs":[45],"achieve":[47],"reasonable":[49],"accuracy":[50],"and":[51],"can":[52],"be":[53],"computationally":[54],"excessive.":[55],"In":[56],"this":[57,74],"paper":[58],"we":[59,91],"formulate":[60],"alternative":[62],"based":[64],"on":[65],"theory":[67],"Random":[69],"Dynamical":[70],"Systems":[71],"solve":[73],"problem.":[75],"Using":[76],"properties":[78],"invariant":[81],"measure":[82],"Perron-Frobenius":[85,115],"operator":[86],"for":[87,111,122],"systems":[90],"obtain":[92,106],"simple":[94],"characterization":[95],"distribution.":[99],"state":[101,123],"space":[102,124],"discretized":[104],"finite":[108],"dimensional":[109,114],"approximation":[110],"infinite":[113],"operator.":[116],"Furthermore,":[117],"efficient":[119],"subdivision":[120],"algorithm":[121],"partition":[125],"discussed.":[127],"demonstrated":[131],"through":[132],"catalytic":[134],"reactor":[135]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
