{"id":"https://openalex.org/W2938029150","doi":"https://doi.org/10.1145/3302504.3311810","title":"Robust invariant sets generation for state-constrained perturbed polynomial systems","display_name":"Robust invariant sets generation for state-constrained perturbed polynomial systems","publication_year":2019,"publication_date":"2019-04-08","ids":{"openalex":"https://openalex.org/W2938029150","doi":"https://doi.org/10.1145/3302504.3311810","mag":"2938029150"},"language":"en","primary_location":{"id":"doi:10.1145/3302504.3311810","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3302504.3311810","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control","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/A5100781916","display_name":"Xue Bai","orcid":"https://orcid.org/0000-0001-9717-846X"},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bai Xue","raw_affiliation_strings":["CAS, Beijing, China"],"affiliations":[{"raw_affiliation_string":"CAS, Beijing, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058964600","display_name":"Qiuye Wang","orcid":"https://orcid.org/0000-0001-5138-3273"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Qiuye Wang","raw_affiliation_strings":["CAS, Beijing, China and University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"CAS, Beijing, China and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026435847","display_name":"Naijun Zhan","orcid":"https://orcid.org/0000-0003-3298-3817"},"institutions":[{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naijun Zhan","raw_affiliation_strings":["CAS, Beijing, China and University of Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"CAS, Beijing, China and University of Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089746112","display_name":"Martin Fr\u00e4nzle","orcid":"https://orcid.org/0000-0002-9138-8340"},"institutions":[{"id":"https://openalex.org/I129877168","display_name":"Carl von Ossietzky Universit\u00e4t Oldenburg","ror":"https://ror.org/033n9gh91","country_code":"DE","type":"education","lineage":["https://openalex.org/I129877168"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Martin Fr\u00e4nzle","raw_affiliation_strings":["Carl von Ossietzky Universit\u00e4t Oldenburg, Oldenburg, Germany"],"affiliations":[{"raw_affiliation_string":"Carl von Ossietzky Universit\u00e4t Oldenburg, Oldenburg, Germany","institution_ids":["https://openalex.org/I129877168"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5100781916"],"corresponding_institution_ids":["https://openalex.org/I19820366"],"apc_list":null,"apc_paid":null,"fwci":2.4947,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.89340436,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"128","last_page":"137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.998199999332428,"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":0.998199999332428,"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":0.9916999936103821,"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/T10142","display_name":"Formal Methods in Verification","score":0.9890999794006348,"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/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.6772168278694153},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6519075632095337},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6431548595428467},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6250311732292175},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6207830309867859},{"id":"https://openalex.org/keywords/reachability","display_name":"Reachability","score":0.6059315800666809},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4868104159832001},{"id":"https://openalex.org/keywords/robust-control","display_name":"Robust control","score":0.4562032222747803},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.41201531887054443},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36703407764434814},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3062899112701416},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25364014506340027},{"id":"https://openalex.org/keywords/control-system","display_name":"Control system","score":0.18175482749938965},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16072487831115723}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.6772168278694153},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6519075632095337},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6431548595428467},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6250311732292175},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6207830309867859},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.6059315800666809},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4868104159832001},{"id":"https://openalex.org/C31531917","wikidata":"https://www.wikidata.org/wiki/Q915157","display_name":"Robust control","level":3,"score":0.4562032222747803},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.41201531887054443},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36703407764434814},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3062899112701416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25364014506340027},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.18175482749938965},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16072487831115723},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3302504.3311810","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3302504.3311810","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W168874853","https://openalex.org/W584400962","https://openalex.org/W1238092070","https://openalex.org/W1487586009","https://openalex.org/W1498729261","https://openalex.org/W1678380195","https://openalex.org/W1879112630","https://openalex.org/W1880805667","https://openalex.org/W1964345118","https://openalex.org/W1973425711","https://openalex.org/W1975236902","https://openalex.org/W1981285936","https://openalex.org/W2004902288","https://openalex.org/W2026650633","https://openalex.org/W2048644096","https://openalex.org/W2072974724","https://openalex.org/W2077883650","https://openalex.org/W2090501324","https://openalex.org/W2090921058","https://openalex.org/W2106816694","https://openalex.org/W2111216640","https://openalex.org/W2116364955","https://openalex.org/W2119974577","https://openalex.org/W2137258051","https://openalex.org/W2141616022","https://openalex.org/W2167019375","https://openalex.org/W2179970775","https://openalex.org/W2268971570","https://openalex.org/W2295906355","https://openalex.org/W2313706817","https://openalex.org/W2317926736","https://openalex.org/W2337661843","https://openalex.org/W2536620281","https://openalex.org/W2555697178","https://openalex.org/W2612952478","https://openalex.org/W2624196447","https://openalex.org/W2796287609","https://openalex.org/W2796295393","https://openalex.org/W2964040381","https://openalex.org/W3210839039","https://openalex.org/W4245376853","https://openalex.org/W4251849361","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2991352819","https://openalex.org/W2159417485","https://openalex.org/W1876742824","https://openalex.org/W2025307894","https://openalex.org/W2734671350","https://openalex.org/W4386132307","https://openalex.org/W4321471503","https://openalex.org/W2552092901","https://openalex.org/W1668532340","https://openalex.org/W2054061677"],"abstract_inverted_index":{"In":[0],"this":[1,54],"paper":[2],"we":[3],"study":[4],"the":[5,18,41,47,59,65,70,86,90,98,115,138],"problem":[6],"of":[7,29,46,53,69,85,92,105,114,140],"computing":[8],"robust":[9,23,61,117,131],"invariant":[10,24,62,118,132],"sets":[11],"for":[12,101],"state-constrained":[13],"perturbed":[14],"polynomial":[15],"systems":[16],"within":[17],"Hamilton-Jacobi":[19],"reachability":[20],"framework.":[21],"A":[22],"set":[25,28,63,68],"is":[26,56],"a":[27,76,123],"states":[30],"such":[31],"that":[32],"every":[33],"possible":[34],"trajectory":[35],"starting":[36],"from":[37],"it":[38],"never":[39],"violates":[40],"given":[42],"state":[43,106],"constraint,":[44],"irrespective":[45],"actual":[48],"perturbation.":[49],"The":[50,80],"main":[51],"contribution":[52],"work":[55],"to":[57,75,96,110,129],"describe":[58],"maximal":[60,116],"as":[64],"zero":[66],"level":[67],"unique":[71],"Lipschitz-continuous":[72],"viscosity":[73,87],"solution":[74,88],"Hamilton-Jacobi-Bellman":[77],"(HJB)":[78],"equation.":[79],"continuity":[81],"and":[82],"uniqueness":[83],"property":[84],"facilitates":[89],"use":[91],"existing":[93],"numerical":[94],"methods":[95],"solve":[97],"HJB":[99],"equation":[100],"an":[102,112],"appropriate":[103],"number":[104],"variables":[107],"in":[108],"order":[109],"obtain":[111],"approximation":[113],"set.":[119],"We":[120],"furthermore":[121],"propose":[122],"method":[124],"based":[125],"on":[126],"semi-definite":[127],"programming":[128],"synthesize":[130],"sets.":[133],"Some":[134],"illustrative":[135],"examples":[136],"demonstrate":[137],"performance":[139],"our":[141],"methods.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
