{"id":"https://openalex.org/W1510867725","doi":"https://doi.org/10.23919/ecc.2009.7074386","title":"A computational method for non-convex reachable sets using optimal control","display_name":"A computational method for non-convex reachable sets using optimal control","publication_year":2009,"publication_date":"2009-08-01","ids":{"openalex":"https://openalex.org/W1510867725","doi":"https://doi.org/10.23919/ecc.2009.7074386","mag":"1510867725"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2009.7074386","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2009.7074386","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":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037003187","display_name":"Robert Baier","orcid":"https://orcid.org/0000-0002-2531-0182"},"institutions":[{"id":"https://openalex.org/I54009628","display_name":"University of Bayreuth","ror":"https://ror.org/0234wmv40","country_code":"DE","type":"education","lineage":["https://openalex.org/I54009628"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Robert Baier","raw_affiliation_strings":["Department of Mathematics, University of Bayreuth, Bayreuth, Germany","Department of Mathematics, University of Bayreuth, 95440, Germany"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Bayreuth, Bayreuth, Germany","institution_ids":["https://openalex.org/I54009628"]},{"raw_affiliation_string":"Department of Mathematics, University of Bayreuth, 95440, Germany","institution_ids":["https://openalex.org/I54009628"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011281312","display_name":"Matthias Gerdts","orcid":"https://orcid.org/0000-0001-8674-5764"},"institutions":[{"id":"https://openalex.org/I25974101","display_name":"University of W\u00fcrzburg","ror":"https://ror.org/00fbnyb24","country_code":"DE","type":"education","lineage":["https://openalex.org/I25974101"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthias Gerdts","raw_affiliation_strings":["Institute of Mathematics, University of W\u00fcrzburg, W\u00fcrzburg, Germany","Institute of Mathematics, University of W\u00fcrzburg, Am Hubland, 97074 Germany"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of W\u00fcrzburg, W\u00fcrzburg, Germany","institution_ids":["https://openalex.org/I25974101"]},{"raw_affiliation_string":"Institute of Mathematics, University of W\u00fcrzburg, Am Hubland, 97074 Germany","institution_ids":["https://openalex.org/I25974101"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5037003187"],"corresponding_institution_ids":["https://openalex.org/I54009628"],"apc_list":null,"apc_paid":null,"fwci":3.845,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.92805117,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"97","last_page":"102"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9965000152587891,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9965000152587891,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.993399977684021,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9933000206947327,"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/discretization","display_name":"Discretization","score":0.8350558876991272},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7021482586860657},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5905336141586304},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5765689611434937},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5635161399841309},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5583921074867249},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5103439688682556},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5052404999732971},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.47902315855026245},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.45065802335739136},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.442852258682251},{"id":"https://openalex.org/keywords/controllability","display_name":"Controllability","score":0.4290798604488373},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4082396626472473},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4049660563468933},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.3539546728134155},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.226241797208786},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22609972953796387}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8350558876991272},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7021482586860657},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5905336141586304},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5765689611434937},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5635161399841309},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5583921074867249},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5103439688682556},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5052404999732971},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.47902315855026245},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.45065802335739136},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.442852258682251},{"id":"https://openalex.org/C48209547","wikidata":"https://www.wikidata.org/wiki/Q1331104","display_name":"Controllability","level":2,"score":0.4290798604488373},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4082396626472473},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4049660563468933},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.3539546728134155},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.226241797208786},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22609972953796387},{"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},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.23919/ecc.2009.7074386","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2009.7074386","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:epub.uni-bayreuth.de:5580","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400362","display_name":"EPub Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Preprint, Postprint"},{"id":"pmh:oai:eref.uni-bayreuth.de:63254","is_oa":false,"landing_page_url":"https://eref.uni-bayreuth.de/63254/","pdf_url":null,"source":{"id":"https://openalex.org/S4377196442","display_name":"ERef Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Aufsatz in einem Buch"}],"best_oa_location":{"id":"pmh:oai:epub.uni-bayreuth.de:5580","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400362","display_name":"EPub Bayreuth (University of Bayreuth)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I54009628","host_organization_name":"University of Bayreuth","host_organization_lineage":["https://openalex.org/I54009628"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Preprint, Postprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W622304541","https://openalex.org/W1512691241","https://openalex.org/W1585773866","https://openalex.org/W1586568018","https://openalex.org/W1726255445","https://openalex.org/W1967773574","https://openalex.org/W1978864877","https://openalex.org/W1983540877","https://openalex.org/W1985115318","https://openalex.org/W2012638722","https://openalex.org/W2018816843","https://openalex.org/W2019989441","https://openalex.org/W2020254113","https://openalex.org/W2024730047","https://openalex.org/W2031291057","https://openalex.org/W2034033019","https://openalex.org/W2059447468","https://openalex.org/W2070604890","https://openalex.org/W2163561970","https://openalex.org/W2433888356","https://openalex.org/W2519129372","https://openalex.org/W3029645440","https://openalex.org/W3135177434"],"related_works":["https://openalex.org/W2054831413","https://openalex.org/W1999673819","https://openalex.org/W3209184047","https://openalex.org/W2026024153","https://openalex.org/W1942635442","https://openalex.org/W4237454804","https://openalex.org/W1990421243","https://openalex.org/W2170835896","https://openalex.org/W2110547027","https://openalex.org/W2539338955"],"abstract_inverted_index":{"A":[0],"computational":[1],"method":[2,16],"for":[3,9,76],"the":[4,23,71],"approximation":[5],"of":[6,22],"reachable":[7,78],"sets":[8,79],"non-linear":[10,62],"dynamic":[11,72],"systems":[12],"is":[13,17,58],"suggested.":[14],"The":[15,32],"based":[18],"on":[19],"a":[20,27,44,53],"discretization":[21,46],"interesting":[24],"region":[25],"and":[26,56,67],"projection":[28],"onto":[29],"grid":[30],"points.":[31],"projections":[33],"require":[34],"to":[35,60,70],"solve":[36],"optimal":[37,49,86],"control":[38,50,65,87],"problems":[39,51],"which":[40],"are":[41,80],"solved":[42],"by":[43],"direct":[45],"approach.":[47],"These":[48],"allow":[52],"flexible":[54],"formulation":[55],"it":[57],"possible":[59],"add":[61],"state":[63],"and/or":[64],"constraints":[66],"boundary":[68],"conditions":[69],"system.":[73],"Numerical":[74],"results":[75],"non-convex":[77],"presented.":[81],"Possible":[82],"applications":[83],"include":[84],"robust":[85],"problems.":[88]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}