{"id":"https://openalex.org/W4400187977","doi":"https://doi.org/10.1109/lcsys.2024.3421194","title":"Inner Approximations of Reachable Sets for Nonlinear Systems Using the Minkowski Difference","display_name":"Inner Approximations of Reachable Sets for Nonlinear Systems Using the Minkowski Difference","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4400187977","doi":"https://doi.org/10.1109/lcsys.2024.3421194"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2024.3421194","is_oa":true,"landing_page_url":"https://doi.org/10.1109/lcsys.2024.3421194","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1109/lcsys.2024.3421194","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5090416908","display_name":"Mark Wetzlinger","orcid":"https://orcid.org/0000-0002-2794-5077"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Mark Wetzlinger","raw_affiliation_strings":["School of Computation, Information and Technology, Technical University of Munich, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"School of Computation, Information and Technology, Technical University of Munich, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070444064","display_name":"Adrian Kulmburg","orcid":"https://orcid.org/0000-0001-6579-2983"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Adrian Kulmburg","raw_affiliation_strings":["School of Computation, Information and Technology, Technical University of Munich, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"School of Computation, Information and Technology, Technical University of Munich, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005383495","display_name":"Matthias Althoff","orcid":"https://orcid.org/0000-0003-3733-842X"},"institutions":[{"id":"https://openalex.org/I62916508","display_name":"Technical University of Munich","ror":"https://ror.org/02kkvpp62","country_code":"DE","type":"education","lineage":["https://openalex.org/I62916508"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Matthias Althoff","raw_affiliation_strings":["School of Computation, Information and Technology, Technical University of Munich, Garching, Germany"],"affiliations":[{"raw_affiliation_string":"School of Computation, Information and Technology, Technical University of Munich, Garching, Germany","institution_ids":["https://openalex.org/I62916508"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5090416908"],"corresponding_institution_ids":["https://openalex.org/I62916508"],"apc_list":null,"apc_paid":null,"fwci":0.3617,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.60896556,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"8","issue":null,"first_page":"2033","last_page":"2038"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"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"}},"topics":[{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T10126","display_name":"Logic, programming, and type systems","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11178","display_name":"Receptor Mechanisms and Signaling","score":0.9660999774932861,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.9091985821723938},{"id":"https://openalex.org/keywords/minkowski-addition","display_name":"Minkowski addition","score":0.8632000684738159},{"id":"https://openalex.org/keywords/minkowski-space","display_name":"Minkowski space","score":0.7171322107315063},{"id":"https://openalex.org/keywords/polytope","display_name":"Polytope","score":0.6931904554367065},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6016141176223755},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.5851927995681763},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5617454648017883},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5282037854194641},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5237412452697754},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5215913653373718},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4648723900318146},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42613619565963745},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3607815206050873},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3078376054763794},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.27910393476486206},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.22217050194740295},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.18182742595672607},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1447359025478363},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08387348055839539},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06200820207595825}],"concepts":[{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.9091985821723938},{"id":"https://openalex.org/C10233890","wikidata":"https://www.wikidata.org/wiki/Q1322294","display_name":"Minkowski addition","level":3,"score":0.8632000684738159},{"id":"https://openalex.org/C79464548","wikidata":"https://www.wikidata.org/wiki/Q464794","display_name":"Minkowski space","level":2,"score":0.7171322107315063},{"id":"https://openalex.org/C145691206","wikidata":"https://www.wikidata.org/wiki/Q747980","display_name":"Polytope","level":2,"score":0.6931904554367065},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6016141176223755},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.5851927995681763},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5617454648017883},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5282037854194641},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5237412452697754},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5215913653373718},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4648723900318146},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42613619565963745},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3607815206050873},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3078376054763794},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27910393476486206},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.22217050194740295},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.18182742595672607},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1447359025478363},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08387348055839539},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06200820207595825},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"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":2,"locations":[{"id":"doi:10.1109/lcsys.2024.3421194","is_oa":true,"landing_page_url":"https://doi.org/10.1109/lcsys.2024.3421194","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems Letters","raw_type":"journal-article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1749456","is_oa":true,"landing_page_url":"https://mediatum.ub.tum.de/1749456","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"ConferencePaper"}],"best_oa_location":{"id":"doi:10.1109/lcsys.2024.3421194","is_oa":true,"landing_page_url":"https://doi.org/10.1109/lcsys.2024.3421194","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Control Systems Letters","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6838856034","display_name":null,"funder_award_id":"817629","funder_id":"https://openalex.org/F4320334678","funder_display_name":"European Research Council"}],"funders":[{"id":"https://openalex.org/F4320334678","display_name":"European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1866311589","https://openalex.org/W1967008192","https://openalex.org/W2019987083","https://openalex.org/W2023842680","https://openalex.org/W2042835403","https://openalex.org/W2095233962","https://openalex.org/W2104730516","https://openalex.org/W2105089101","https://openalex.org/W2123640521","https://openalex.org/W2158451642","https://openalex.org/W2300621294","https://openalex.org/W2483544051","https://openalex.org/W2568852336","https://openalex.org/W2576277975","https://openalex.org/W2606692557","https://openalex.org/W2606891832","https://openalex.org/W2750147881","https://openalex.org/W2766658289","https://openalex.org/W2777392906","https://openalex.org/W2807455070","https://openalex.org/W2936781873","https://openalex.org/W2963530480","https://openalex.org/W3031094646","https://openalex.org/W3037216378","https://openalex.org/W3086849158","https://openalex.org/W3119746089","https://openalex.org/W3127322525","https://openalex.org/W4238726034","https://openalex.org/W4239940594","https://openalex.org/W4290087487","https://openalex.org/W4388093113","https://openalex.org/W6743558609","https://openalex.org/W6746969752","https://openalex.org/W6857335438","https://openalex.org/W7066118332"],"related_works":["https://openalex.org/W3128178508","https://openalex.org/W2560815480","https://openalex.org/W2962710660","https://openalex.org/W2112785014","https://openalex.org/W2286777929","https://openalex.org/W4293050169","https://openalex.org/W2078958623","https://openalex.org/W2950428426","https://openalex.org/W2494974567","https://openalex.org/W4255234857"],"abstract_inverted_index":{"Reachability":[0],"analysis":[1],"is":[2],"a":[3,10,73,82,94],"formal":[4],"method":[5],"that":[6,27],"rigorously":[7],"proves":[8],"whether":[9],"dynamical":[11],"system":[12],"can":[13],"reach":[14],"certain":[15],"states.":[16],"Inner":[17],"approximations":[18,66],"of":[19,41,57,84,114],"the":[20,39,58,69,100,112],"exact":[21],"reachable":[22,30,59],"set":[23,90],"contain":[24],"only":[25],"states":[26],"are":[28,32],"definitely":[29],"and":[31,86],"therefore":[33],"used":[34],"to":[35],"falsify":[36],"specifications.":[37],"While":[38],"majority":[40],"state-of-the-art":[42,106],"approaches":[43,107],"for":[44,76],"nonlinear":[45,77],"systems":[46],"obtain":[47,63],"an":[48,54],"inner":[49,65],"approximation":[50,56],"via":[51],"first":[52],"computing":[53],"outer":[55],"set,":[60],"we":[61],"directly":[62],"sound":[64],"by":[67],"using":[68],"Minkowski":[70],"difference":[71],"in":[72,93,99],"reachability":[74],"algorithm":[75],"systems.":[78],"Our":[79],"implementation":[80],"uses":[81],"combination":[83],"polytopes":[85],"constrained":[87],"zonotopes":[88],"as":[89],"representations,":[91],"resulting":[92],"low":[95],"polynomial":[96],"time":[97],"complexity":[98],"state":[101],"dimension.":[102],"A":[103],"comparison":[104],"with":[105],"on":[108],"several":[109],"benchmarks":[110],"demonstrates":[111],"advantages":[113],"our":[115],"approach.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2024-07-02T00:00:00"}