{"id":"https://openalex.org/W4389670720","doi":"https://doi.org/10.1145/3613347.3613365","title":"Bernstein Coefficients for Computing Rational Lyapunov and Control Functions of Dynamical Systems","display_name":"Bernstein Coefficients for Computing Rational Lyapunov and Control Functions of Dynamical Systems","publication_year":2023,"publication_date":"2023-07-14","ids":{"openalex":"https://openalex.org/W4389670720","doi":"https://doi.org/10.1145/3613347.3613365"},"language":"en","primary_location":{"id":"doi:10.1145/3613347.3613365","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3613347.3613365","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2023 6th International Conference on Mathematics and Statistics","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/A5009403196","display_name":"Tareq Hamadneh","orcid":"https://orcid.org/0000-0003-1867-8111"},"institutions":[{"id":"https://openalex.org/I145019703","display_name":"Al-Zaytoonah University of Jordan","ror":"https://ror.org/04a5b0p13","country_code":"JO","type":"education","lineage":["https://openalex.org/I145019703"]}],"countries":["JO"],"is_corresponding":true,"raw_author_name":"Tareq Hamadneh","raw_affiliation_strings":["Mathematics/ IT/M, Al Zaytoonah University of Jordan, Jordan"],"raw_orcid":"https://orcid.org/0000-0003-1867-8111","affiliations":[{"raw_affiliation_string":"Mathematics/ IT/M, Al Zaytoonah University of Jordan, Jordan","institution_ids":["https://openalex.org/I145019703"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113070071","display_name":"Ibraheem Abu-Falahah","orcid":null},"institutions":[{"id":"https://openalex.org/I145019703","display_name":"Al-Zaytoonah University of Jordan","ror":"https://ror.org/04a5b0p13","country_code":"JO","type":"education","lineage":["https://openalex.org/I145019703"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Ibraheem Abu-Falahah","raw_affiliation_strings":["Mathematics, Al Zaytoonah University of Jordan, Jordan"],"raw_orcid":"https://orcid.org/0000-0001-7650-5863","affiliations":[{"raw_affiliation_string":"Mathematics, Al Zaytoonah University of Jordan, Jordan","institution_ids":["https://openalex.org/I145019703"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088258408","display_name":"Mohammad Hamadneh","orcid":"https://orcid.org/0009-0009-7456-9885"},"institutions":[{"id":"https://openalex.org/I156983542","display_name":"Jordan University of Science and Technology","ror":"https://ror.org/03y8mtb59","country_code":"JO","type":"education","lineage":["https://openalex.org/I156983542"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Mohammad D. Hamadneh","raw_affiliation_strings":["Mathematics, Jordan University of Science and Technology, Jordan"],"raw_orcid":"https://orcid.org/0009-0009-7456-9885","affiliations":[{"raw_affiliation_string":"Mathematics, Jordan University of Science and Technology, Jordan","institution_ids":["https://openalex.org/I156983542"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091006504","display_name":"Amjed Zraiqat","orcid":"https://orcid.org/0000-0002-0838-4382"},"institutions":[{"id":"https://openalex.org/I145019703","display_name":"Al-Zaytoonah University of Jordan","ror":"https://ror.org/04a5b0p13","country_code":"JO","type":"education","lineage":["https://openalex.org/I145019703"]}],"countries":["JO"],"is_corresponding":false,"raw_author_name":"Amjed Zraiqat","raw_affiliation_strings":["Mathematics, Al Zaytoonah University of Jordan, Jordan"],"raw_orcid":"https://orcid.org/0000-0002-0838-4382","affiliations":[{"raw_affiliation_string":"Mathematics, Al Zaytoonah University of Jordan, Jordan","institution_ids":["https://openalex.org/I145019703"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5009403196"],"corresponding_institution_ids":["https://openalex.org/I145019703"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.27143065,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"114","last_page":"119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9944999814033508,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9825999736785889,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bernstein-polynomial","display_name":"Bernstein polynomial","score":0.8434010744094849},{"id":"https://openalex.org/keywords/monomial","display_name":"Monomial","score":0.6698051691055298},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6570903062820435},{"id":"https://openalex.org/keywords/rational-function","display_name":"Rational function","score":0.6330410242080688},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6144468784332275},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5984822511672974},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5683444738388062},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5217986106872559},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.4479484260082245},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.37322038412094116},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3385593891143799},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2553367614746094},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.0879959762096405}],"concepts":[{"id":"https://openalex.org/C34179328","wikidata":"https://www.wikidata.org/wiki/Q826841","display_name":"Bernstein polynomial","level":2,"score":0.8434010744094849},{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.6698051691055298},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6570903062820435},{"id":"https://openalex.org/C75190567","wikidata":"https://www.wikidata.org/wiki/Q41237","display_name":"Rational function","level":2,"score":0.6330410242080688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6144468784332275},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5984822511672974},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5683444738388062},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5217986106872559},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.4479484260082245},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.37322038412094116},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3385593891143799},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2553367614746094},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0879959762096405},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/3613347.3613365","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3613347.3613365","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2023 6th International Conference on Mathematics and Statistics","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":7,"referenced_works":["https://openalex.org/W1483893502","https://openalex.org/W1978884939","https://openalex.org/W2025810010","https://openalex.org/W2502360843","https://openalex.org/W2888919622","https://openalex.org/W3025957244","https://openalex.org/W4281570361"],"related_works":["https://openalex.org/W2399505800","https://openalex.org/W333749553","https://openalex.org/W3121681491","https://openalex.org/W1966623661","https://openalex.org/W2296409857","https://openalex.org/W2946568754","https://openalex.org/W2378159473","https://openalex.org/W4386257493","https://openalex.org/W2099581135","https://openalex.org/W2951047924"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"address":[4],"the":[5,35,48,54,62],"Bernstein":[6,27,40,57,66],"expansion":[7],"of":[8,42,50,65],"rational":[9,18,26,39,51],"polynomial":[10],"continuous":[11],"dynamical":[12],"systems":[13],"over":[14],"simplices.":[15],"We":[16],"consider":[17],"Lyapunov":[19],"functions":[20,31,52],"and":[21,37,56],"controllers":[22],"both":[23],"expanded":[24],"into":[25],"form.":[28],"Rational":[29],"control":[30],"are":[32,59],"optimized":[33],"by":[34],"smallest":[36],"largest":[38],"coefficients":[41],"maximum":[43,63],"degree.":[44],"Bounds":[45],"for":[46],"certifying":[47],"existence":[49],"in":[53],"monomial":[55],"forms":[58],"given.":[60],"Subsequently,":[61],"degree":[64],"basis":[67],"is":[68],"sufficiently":[69],"optimized.":[70]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
