{"id":"https://openalex.org/W2945540138","doi":"https://doi.org/10.1109/tcst.2019.2908938","title":"Stochastic Spacecraft Trajectory Optimization With the Consideration of Chance Constraints","display_name":"Stochastic Spacecraft Trajectory Optimization With the Consideration of Chance Constraints","publication_year":2019,"publication_date":"2019-05-23","ids":{"openalex":"https://openalex.org/W2945540138","doi":"https://doi.org/10.1109/tcst.2019.2908938","mag":"2945540138"},"language":"en","primary_location":{"id":"doi:10.1109/tcst.2019.2908938","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2019.2908938","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"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 Control Systems Technology","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.lib.cranfield.ac.uk/handle/1826/15269","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5024866488","display_name":"Runqi Chai","orcid":"https://orcid.org/0000-0003-4083-8863"},"institutions":[{"id":"https://openalex.org/I82284825","display_name":"Cranfield University","ror":"https://ror.org/05cncd958","country_code":"GB","type":"education","lineage":["https://openalex.org/I82284825"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Runqi Chai","raw_affiliation_strings":["School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K"],"raw_orcid":"https://orcid.org/0000-0003-4083-8863","affiliations":[{"raw_affiliation_string":"School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K","institution_ids":["https://openalex.org/I82284825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102861951","display_name":"Al Savvaris","orcid":"https://orcid.org/0000-0003-3210-5838"},"institutions":[{"id":"https://openalex.org/I82284825","display_name":"Cranfield University","ror":"https://ror.org/05cncd958","country_code":"GB","type":"education","lineage":["https://openalex.org/I82284825"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Al Savvaris","raw_affiliation_strings":["School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K","institution_ids":["https://openalex.org/I82284825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085012064","display_name":"Antonios Tsourdos","orcid":"https://orcid.org/0000-0002-3966-7633"},"institutions":[{"id":"https://openalex.org/I82284825","display_name":"Cranfield University","ror":"https://ror.org/05cncd958","country_code":"GB","type":"education","lineage":["https://openalex.org/I82284825"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Antonios Tsourdos","raw_affiliation_strings":["School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K"],"raw_orcid":"https://orcid.org/0000-0002-3966-7633","affiliations":[{"raw_affiliation_string":"School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield, U.K","institution_ids":["https://openalex.org/I82284825"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070349528","display_name":"Senchun Chai","orcid":"https://orcid.org/0000-0003-1910-1795"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Senchun Chai","raw_affiliation_strings":["School of Automation, Beijing Institute of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-1910-1795","affiliations":[{"raw_affiliation_string":"School of Automation, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064231378","display_name":"Yuanqing Xia","orcid":"https://orcid.org/0000-0002-5977-4911"},"institutions":[{"id":"https://openalex.org/I125839683","display_name":"Beijing Institute of Technology","ror":"https://ror.org/01skt4w74","country_code":"CN","type":"education","lineage":["https://openalex.org/I125839683","https://openalex.org/I890469752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanqing Xia","raw_affiliation_strings":["School of Automation, Beijing Institute of Technology, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-5977-4911","affiliations":[{"raw_affiliation_string":"School of Automation, Beijing Institute of Technology, Beijing, China","institution_ids":["https://openalex.org/I125839683"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":33.254,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.99244976,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"28","issue":"4","first_page":"1550","last_page":"1559"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11082","display_name":"Spacecraft Dynamics and Control","score":0.9994999766349792,"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/T13855","display_name":"Aerospace Engineering and Control Systems","score":0.9901000261306763,"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/T11701","display_name":"Space Satellite Systems and Control","score":0.9866999983787537,"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/trajectory-optimization","display_name":"Trajectory optimization","score":0.7214186191558838},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.7107651233673096},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.6732537746429443},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6358921527862549},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5690497159957886},{"id":"https://openalex.org/keywords/stochastic-optimization","display_name":"Stochastic optimization","score":0.5387097597122192},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5299260020256042},{"id":"https://openalex.org/keywords/spacecraft","display_name":"Spacecraft","score":0.5296606421470642},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.5207985639572144},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4722292423248291},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.471583753824234},{"id":"https://openalex.org/keywords/stochastic-control","display_name":"Stochastic control","score":0.4284636676311493},{"id":"https://openalex.org/keywords/constrained-optimization","display_name":"Constrained optimization","score":0.42804449796676636},{"id":"https://openalex.org/keywords/stochastic-programming","display_name":"Stochastic programming","score":0.4183763861656189},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3599538803100586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2673553228378296},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.20554789900779724},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.15888944268226624},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.10128286480903625}],"concepts":[{"id":"https://openalex.org/C173246807","wikidata":"https://www.wikidata.org/wiki/Q7833062","display_name":"Trajectory optimization","level":3,"score":0.7214186191558838},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.7107651233673096},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.6732537746429443},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6358921527862549},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5690497159957886},{"id":"https://openalex.org/C194387892","wikidata":"https://www.wikidata.org/wiki/Q1747770","display_name":"Stochastic optimization","level":2,"score":0.5387097597122192},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5299260020256042},{"id":"https://openalex.org/C29829512","wikidata":"https://www.wikidata.org/wiki/Q40218","display_name":"Spacecraft","level":2,"score":0.5296606421470642},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5207985639572144},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4722292423248291},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.471583753824234},{"id":"https://openalex.org/C170131372","wikidata":"https://www.wikidata.org/wiki/Q7617811","display_name":"Stochastic control","level":3,"score":0.4284636676311493},{"id":"https://openalex.org/C55660270","wikidata":"https://www.wikidata.org/wiki/Q5164377","display_name":"Constrained optimization","level":2,"score":0.42804449796676636},{"id":"https://openalex.org/C137631369","wikidata":"https://www.wikidata.org/wiki/Q7617831","display_name":"Stochastic programming","level":2,"score":0.4183763861656189},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3599538803100586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2673553228378296},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.20554789900779724},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.15888944268226624},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.10128286480903625},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tcst.2019.2908938","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcst.2019.2908938","pdf_url":null,"source":{"id":"https://openalex.org/S133363738","display_name":"IEEE Transactions on Control Systems Technology","issn_l":"1063-6536","issn":["1063-6536","1558-0865","2374-0159"],"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 Control Systems Technology","raw_type":"journal-article"},{"id":"pmh:oai:dspace.lib.cranfield.ac.uk:1826/15269","is_oa":true,"landing_page_url":"https://dspace.lib.cranfield.ac.uk/handle/1826/15269","pdf_url":null,"source":{"id":"https://openalex.org/S4306401778","display_name":"CERES (Cranfield University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I82284825","host_organization_name":"Cranfield University","host_organization_lineage":["https://openalex.org/I82284825"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:dspace.lib.cranfield.ac.uk:1826/15269","is_oa":true,"landing_page_url":"https://dspace.lib.cranfield.ac.uk/handle/1826/15269","pdf_url":null,"source":{"id":"https://openalex.org/S4306401778","display_name":"CERES (Cranfield University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I82284825","host_organization_name":"Cranfield University","host_organization_lineage":["https://openalex.org/I82284825"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W647800561","https://openalex.org/W1963788580","https://openalex.org/W1971092617","https://openalex.org/W1984474823","https://openalex.org/W1999131722","https://openalex.org/W2035670438","https://openalex.org/W2057268957","https://openalex.org/W2066031462","https://openalex.org/W2069364408","https://openalex.org/W2085232378","https://openalex.org/W2099506495","https://openalex.org/W2107345353","https://openalex.org/W2110357265","https://openalex.org/W2146380167","https://openalex.org/W2169407687","https://openalex.org/W2339802450","https://openalex.org/W2523897339","https://openalex.org/W2594215104","https://openalex.org/W2654286404","https://openalex.org/W2743593866","https://openalex.org/W2748977773","https://openalex.org/W2750408863","https://openalex.org/W2766803511","https://openalex.org/W2767157617","https://openalex.org/W2774276467","https://openalex.org/W2775403132","https://openalex.org/W2782828584","https://openalex.org/W2786483361","https://openalex.org/W2964111918"],"related_works":["https://openalex.org/W4254717236","https://openalex.org/W2377757044","https://openalex.org/W3160952126","https://openalex.org/W2320103255","https://openalex.org/W798918733","https://openalex.org/W4213167601","https://openalex.org/W163279402","https://openalex.org/W2101287851","https://openalex.org/W2403168774","https://openalex.org/W2281909915"],"abstract_inverted_index":{"This":[0,24],"brief":[1],"investigates":[2],"a":[3,27,66,92],"computational":[4,127],"framework":[5,128],"based":[6],"on":[7],"optimal":[8,52,89],"control":[9,53],"for":[10,91,136],"addressing":[11],"the":[12,19,36,40,45,63,77,88,111,137],"problem":[13,46],"of":[14,21,44],"stochastic":[15,139],"trajectory":[16,37,141],"optimization":[17,64],"with":[18,98],"consideration":[20],"chance":[22],"constraints.":[23,80,103],"design":[25],"employs":[26],"discretization":[28],"technique":[29],"to":[30,57,62,75,86],"parameterize":[31],"uncertain":[32],"variables":[33],"and":[34,68,101,106,125,132],"create":[35],"ensemble.":[38],"Subsequently,":[39],"resulting":[41],"discretized":[42],"version":[43],"is":[47,73,84],"solved":[48],"by":[49],"applying":[50],"standard":[51],"solvers.":[54],"In":[55],"order":[56],"provide":[58],"reliable":[59,131],"gradient":[60],"information":[61],"algorithm,":[65],"smooth":[67],"differentiable":[69],"chance-constraint":[70,113],"approximation":[71],"method":[72],"proposed":[74],"replace":[76],"original":[78],"probability":[79],"The":[81],"established":[82],"methodology":[83],"implemented":[85],"explore":[87],"trajectories":[90],"spacecraft":[93,140],"entry":[94],"flight":[95],"planning":[96,142],"scenario":[97],"noise-perturbed":[99],"dynamics":[100],"probabilistic":[102],"Simulation":[104],"results":[105],"comparative":[107],"studies":[108],"demonstrate":[109],"that":[110],"present":[112],"handling":[114],"strategy":[115],"can":[116,129],"outperform":[117],"other":[118],"existing":[119],"approaches":[120],"analyzed":[121],"in":[122],"this":[123,126],"brief,":[124],"produce":[130],"less":[133],"conservative":[134],"solutions":[135],"chance-constrained":[138],"problem.":[143]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1}],"updated_date":"2026-07-25T09:21:30.201066","created_date":"2025-10-10T00:00:00"}