{"id":"https://openalex.org/W3107606296","doi":"https://doi.org/10.1109/codit49905.2020.9263829","title":"Computation of Positively Invariant Sets of the Duffing System and the Nonlinear Pendulum under Bounded Excitation","display_name":"Computation of Positively Invariant Sets of the Duffing System and the Nonlinear Pendulum under Bounded Excitation","publication_year":2020,"publication_date":"2020-06-29","ids":{"openalex":"https://openalex.org/W3107606296","doi":"https://doi.org/10.1109/codit49905.2020.9263829","mag":"3107606296"},"language":"en","primary_location":{"id":"doi:10.1109/codit49905.2020.9263829","is_oa":false,"landing_page_url":"http://doi.org/10.1109/codit49905.2020.9263829","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 7th International Conference on Control, Decision and Information Technologies (CoDIT)","raw_type":"proceedings-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/A5054405093","display_name":"Klaus R\u00f6benack","orcid":"https://orcid.org/0000-0002-3347-0864"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Klaus Robenack","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5007652627","display_name":"Daniel Gerbet","orcid":"https://orcid.org/0000-0002-8527-8727"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Daniel Gerbet","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054405093"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1328,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45867049,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"218","issue":null,"first_page":"271","last_page":"276"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9509999752044678,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9509999752044678,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9373000264167786,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9354000091552734,"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/nonlinear-system","display_name":"Nonlinear system","score":0.7662528157234192},{"id":"https://openalex.org/keywords/pendulum","display_name":"Pendulum","score":0.7482033967971802},{"id":"https://openalex.org/keywords/intermittency","display_name":"Intermittency","score":0.702564537525177},{"id":"https://openalex.org/keywords/duffing-equation","display_name":"Duffing equation","score":0.6479654908180237},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6158051490783691},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6142516136169434},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6125998497009277},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6036628484725952},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.418737530708313},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4133259057998657},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.330615758895874},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3291091024875641},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28684261441230774},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2340611219406128},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11324194073677063},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.07582366466522217},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.0640363097190857},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06032785773277283}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7662528157234192},{"id":"https://openalex.org/C110639684","wikidata":"https://www.wikidata.org/wiki/Q20702","display_name":"Pendulum","level":2,"score":0.7482033967971802},{"id":"https://openalex.org/C2780388094","wikidata":"https://www.wikidata.org/wiki/Q1666248","display_name":"Intermittency","level":3,"score":0.702564537525177},{"id":"https://openalex.org/C132323500","wikidata":"https://www.wikidata.org/wiki/Q675387","display_name":"Duffing equation","level":3,"score":0.6479654908180237},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6158051490783691},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6142516136169434},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6125998497009277},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6036628484725952},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.418737530708313},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4133259057998657},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.330615758895874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3291091024875641},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28684261441230774},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2340611219406128},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11324194073677063},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.07582366466522217},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.0640363097190857},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06032785773277283},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C196558001","wikidata":"https://www.wikidata.org/wiki/Q190132","display_name":"Turbulence","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/codit49905.2020.9263829","is_oa":false,"landing_page_url":"http://doi.org/10.1109/codit49905.2020.9263829","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 7th International Conference on Control, Decision and Information Technologies (CoDIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W608564660","https://openalex.org/W637874180","https://openalex.org/W840591150","https://openalex.org/W1487127700","https://openalex.org/W1553142094","https://openalex.org/W1561445488","https://openalex.org/W1570787829","https://openalex.org/W1574151794","https://openalex.org/W1597600813","https://openalex.org/W1973667962","https://openalex.org/W1985289520","https://openalex.org/W1986264093","https://openalex.org/W2000040887","https://openalex.org/W2005188216","https://openalex.org/W2010508518","https://openalex.org/W2016056788","https://openalex.org/W2023618328","https://openalex.org/W2026612342","https://openalex.org/W2029030701","https://openalex.org/W2029862252","https://openalex.org/W2039279140","https://openalex.org/W2049724218","https://openalex.org/W2056473089","https://openalex.org/W2056708573","https://openalex.org/W2058236317","https://openalex.org/W2061749308","https://openalex.org/W2064053127","https://openalex.org/W2075591840","https://openalex.org/W2089876099","https://openalex.org/W2104715607","https://openalex.org/W2118894753","https://openalex.org/W2135001101","https://openalex.org/W2154496368","https://openalex.org/W2161706840","https://openalex.org/W2198618549","https://openalex.org/W2312849699","https://openalex.org/W2318268489","https://openalex.org/W2555576087","https://openalex.org/W2589479599","https://openalex.org/W2605543710","https://openalex.org/W2776826490","https://openalex.org/W2871093631","https://openalex.org/W2930483989","https://openalex.org/W2978550584","https://openalex.org/W2979169928","https://openalex.org/W3024307996","https://openalex.org/W4255213956"],"related_works":["https://openalex.org/W2564644595","https://openalex.org/W1589804082","https://openalex.org/W1566002589","https://openalex.org/W2042838258","https://openalex.org/W2075007075","https://openalex.org/W2783018065","https://openalex.org/W1525560163","https://openalex.org/W4387214903","https://openalex.org/W1964264122","https://openalex.org/W3101798938"],"abstract_inverted_index":{"The":[0,40],"Duffing":[1,70],"system":[2,25,71],"and":[3,22,72],"the":[4,65,68,73],"nonlinear":[5,37,74],"pendulum":[6],"are":[7,78],"a":[8,31,57],"comparatively":[9],"simple":[10],"dynamical":[11],"systems":[12],"that":[13],"can":[14,42],"generate":[15],"complex":[16],"dynamics":[17,41],"such":[18],"as":[19],"subharmonics,":[20],"intermittency":[21],"chaos.":[23],"Both":[24],"has":[26],"been":[27],"used":[28],"to":[29,59],"model":[30],"variety":[32],"of":[33,67],"technical":[34],"systems,":[35],"where":[36],"oscillations":[38],"occur.":[39],"usually":[43],"not":[44],"be":[45],"computed":[46],"analytically":[47,61],"but":[48],"only":[49],"simulated":[50],"numerically.":[51],"In":[52],"this":[53],"paper":[54],"we":[55],"provide":[56],"method":[58],"compute":[60],"exact":[62],"bounds":[63],"on":[64],"trajectories":[66],"excited":[69],"pendulum.":[75],"These":[76],"computations":[77],"carried":[79],"out":[80],"using":[81],"quantifier":[82],"elimination.":[83]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}