{"id":"https://openalex.org/W2117623527","doi":"https://doi.org/10.1080/00207171003586914","title":"Trajectory planning for quasilinear parabolic distributed parameter systems based on finite-difference semi-discretisations","display_name":"Trajectory planning for quasilinear parabolic distributed parameter systems based on finite-difference semi-discretisations","publication_year":2010,"publication_date":"2010-05-19","ids":{"openalex":"https://openalex.org/W2117623527","doi":"https://doi.org/10.1080/00207171003586914","mag":"2117623527"},"language":"en","primary_location":{"id":"doi:10.1080/00207171003586914","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207171003586914","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},"type":"article","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/A5078619483","display_name":"Tilman Utz","orcid":null},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"T. Utz","raw_affiliation_strings":["a Automation and Control Institute , Vienna University of Technology , Vienna , Austria","Automation and Control Institute , Vienna University of Technology , Vienna , Austria"],"affiliations":[{"raw_affiliation_string":"a Automation and Control Institute , Vienna University of Technology , Vienna , Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Automation and Control Institute , Vienna University of Technology , Vienna , Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002069913","display_name":"Thomas Meurer","orcid":"https://orcid.org/0000-0002-9175-2157"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"T. Meurer","raw_affiliation_strings":["a Automation and Control Institute , Vienna University of Technology , Vienna , Austria","Automation and Control Institute , Vienna University of Technology , Vienna , Austria"],"affiliations":[{"raw_affiliation_string":"a Automation and Control Institute , Vienna University of Technology , Vienna , Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Automation and Control Institute , Vienna University of Technology , Vienna , Austria","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014193427","display_name":"Andreas Kugi","orcid":"https://orcid.org/0000-0001-7995-1690"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"A. Kugi","raw_affiliation_strings":["a Automation and Control Institute , Vienna University of Technology , Vienna , Austria","Automation and Control Institute , Vienna University of Technology , Vienna , Austria"],"affiliations":[{"raw_affiliation_string":"a Automation and Control Institute , Vienna University of Technology , Vienna , Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Automation and Control Institute , Vienna University of Technology , Vienna , Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5078619483"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":null,"apc_paid":null,"fwci":3.7944,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.93522727,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"83","issue":"6","first_page":"1093","last_page":"1106"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9984999895095825,"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/T11110","display_name":"Stability and Controllability of Differential Equations","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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/flatness","display_name":"Flatness (cosmology)","score":0.828776478767395},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7023428678512573},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6784295439720154},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.677266001701355},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5257340669631958},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5086567997932434},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41845250129699707},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3905811607837677},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21849671006202698},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.10918587446212769},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08531254529953003},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08527633547782898}],"concepts":[{"id":"https://openalex.org/C2778530986","wikidata":"https://www.wikidata.org/wiki/Q5457948","display_name":"Flatness (cosmology)","level":3,"score":0.828776478767395},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7023428678512573},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6784295439720154},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.677266001701355},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5257340669631958},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5086567997932434},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41845250129699707},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3905811607837677},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21849671006202698},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.10918587446212769},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08531254529953003},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08527633547782898},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C26405456","wikidata":"https://www.wikidata.org/wiki/Q338","display_name":"Cosmology","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207171003586914","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207171003586914","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5899999737739563,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320334763","display_name":"Leibniz-Gemeinschaft","ror":"https://ror.org/01n6r0e97"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W104059094","https://openalex.org/W264698278","https://openalex.org/W383892817","https://openalex.org/W1513988648","https://openalex.org/W1877697960","https://openalex.org/W1931049532","https://openalex.org/W1966686724","https://openalex.org/W2024175557","https://openalex.org/W2038175923","https://openalex.org/W2065162502","https://openalex.org/W2065297540","https://openalex.org/W2082009002","https://openalex.org/W2092159572","https://openalex.org/W2129048452","https://openalex.org/W2149678156","https://openalex.org/W2271960839","https://openalex.org/W2524706706","https://openalex.org/W2600679468","https://openalex.org/W2783350696","https://openalex.org/W2918042722","https://openalex.org/W4230168603","https://openalex.org/W4250720901"],"related_works":["https://openalex.org/W2989775562","https://openalex.org/W2002316083","https://openalex.org/W2069749134","https://openalex.org/W2507513082","https://openalex.org/W2953752747","https://openalex.org/W2754413006","https://openalex.org/W2082214929","https://openalex.org/W2008813171","https://openalex.org/W4324119752","https://openalex.org/W4297081795"],"abstract_inverted_index":{"In":[0],"this":[1,79],"contribution,":[2],"a":[3,49,81],"flatness-based":[4],"approach":[5],"is":[6,30,89],"considered":[7],"for":[8,16,48,85],"the":[9,12,33,44,57,86],"solution":[10],"of":[11,26,52],"trajectory":[13,46],"planning":[14,47],"problem":[15],"quasilinear":[17],"parabolic":[18,54],"distributed":[19],"parameter":[20],"systems":[21,66],"(DPS)":[22],"by":[23],"making":[24],"use":[25],"finite-difference":[27],"semi-discretisations.":[28],"It":[29],"shown":[31],"that":[32],"method":[34],"yields":[35],"solutions":[36],"which":[37],"are":[38,75],"equivalent":[39],"to":[40,65],"results":[41,74],"known":[42],"from":[43],"infinite-dimensional":[45],"certain":[50],"class":[51],"quasi-linear":[53],"DPS.":[55],"Furthermore,":[56],"methodology":[58],"being":[59],"proposed":[60],"can":[61],"also":[62],"be":[63],"applied":[64],"with":[67],"general":[68],"analytic":[69],"nonlinearities.":[70],"As":[71],"analytical":[72],"convergence":[73,87],"not":[76],"available":[77],"in":[78],"case,":[80],"numerical":[82],"test":[83],"criterion":[84],"behaviour":[88],"suggested.":[90]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-03-31T07:56:22.981413","created_date":"2025-10-10T00:00:00"}
