{"id":"https://openalex.org/W7130430203","doi":"https://doi.org/10.1007/s00498-026-00437-z","title":"Hierarchical controller synthesis using ($$\\upgamma ,\\updelta $$)-Similarity","display_name":"Hierarchical controller synthesis using ($$\\upgamma ,\\updelta $$)-Similarity","publication_year":2026,"publication_date":"2026-02-18","ids":{"openalex":"https://openalex.org/W7130430203","doi":"https://doi.org/10.1007/s00498-026-00437-z","pmid":"https://pubmed.ncbi.nlm.nih.gov/42272929"},"language":"en","primary_location":{"id":"doi:10.1007/s00498-026-00437-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00498-026-00437-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00498-026-00437-z.pdf","source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00498-026-00437-z.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051158060","display_name":"Armin Pirastehzad","orcid":"https://orcid.org/0000-0002-8238-7258"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":true,"raw_author_name":"Armin Pirastehzad","raw_affiliation_strings":["Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9700 AK Groningen, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9700 AK Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126323738","display_name":"Arjan van der Schaft","orcid":null},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Arjan van der Schaft","raw_affiliation_strings":["Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9700 AK Groningen, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9700 AK Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083507299","display_name":"Bart Besselink","orcid":"https://orcid.org/0000-0001-5194-3306"},"institutions":[{"id":"https://openalex.org/I169381384","display_name":"University of Groningen","ror":"https://ror.org/012p63287","country_code":"NL","type":"education","lineage":["https://openalex.org/I169381384"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Bart Besselink","raw_affiliation_strings":["Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9700 AK Groningen, The Netherlands"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, 9700 AK Groningen, The Netherlands","institution_ids":["https://openalex.org/I169381384"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051158060"],"corresponding_institution_ids":["https://openalex.org/I169381384"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22448281,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"38","issue":"2","first_page":"335","last_page":"363"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.48590001463890076,"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":0.48590001463890076,"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/T11125","display_name":"Petri Nets in System Modeling","score":0.3449999988079071,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.05299999937415123,"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/controller","display_name":"Controller (irrigation)","score":0.7883999943733215},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6567000150680542},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.6061999797821045},{"id":"https://openalex.org/keywords/abstraction","display_name":"Abstraction","score":0.5885999798774719},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5712000131607056},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5694000124931335},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.5490999817848206}],"concepts":[{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.7883999943733215},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6567000150680542},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.6061999797821045},{"id":"https://openalex.org/C124304363","wikidata":"https://www.wikidata.org/wiki/Q673661","display_name":"Abstraction","level":2,"score":0.5885999798774719},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5712000131607056},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5694000124931335},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.5490999817848206},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5103999972343445},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C161362739","wikidata":"https://www.wikidata.org/wiki/Q2301555","display_name":"Open-loop controller","level":3,"score":0.42969998717308044},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.42340001463890076},{"id":"https://openalex.org/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.3930000066757202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3700000047683716},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.2689000070095062}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s00498-026-00437-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00498-026-00437-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00498-026-00437-z.pdf","source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"},{"id":"pmid:42272929","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/42272929","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of control, signals, and systems : MCSS","raw_type":null},{"id":"pmh:oai:pure.rug.nl:openaire/e2d63c45-1376-4b2d-89d3-268d516f88ca","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/e2d63c45-1376-4b2d-89d3-268d516f88ca","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Pirastehzad, A, van der Schaft, A & Besselink, B 2026, 'Hierarchical controller synthesis using (\u03b3,\u03b4)-Similarity', Mathematics of Control, Signals, and Systems, vol. 38, pp. 335-363. https://doi.org/10.1007/s00498-026-00437-z","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:pubmedcentral.nih.gov:13246880","is_oa":true,"landing_page_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC13246880/","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Math Control Signal Syst","raw_type":"Text"},{"id":"pmh:oai:pure.rug.nl:publications/e2d63c45-1376-4b2d-89d3-268d516f88ca","is_oa":true,"landing_page_url":"https://hdl.handle.net/11370/e2d63c45-1376-4b2d-89d3-268d516f88ca","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Pirastehzad, A, van der Schaft, A & Besselink, B 2026, 'Hierarchical controller synthesis using (\u03b3,\u03b4)-Similarity', Mathematics of Control, Signals, and Systems, vol. 38, pp. 335-363. https://doi.org/10.1007/s00498-026-00437-z","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s00498-026-00437-z","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00498-026-00437-z","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00498-026-00437-z.pdf","source":{"id":"https://openalex.org/S88345224","display_name":"Mathematics of Control Signals and Systems","issn_l":"0932-4194","issn":["0932-4194","1435-568X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Control, Signals, and Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1502848176","display_name":null,"funder_award_id":"P18-03","funder_id":"https://openalex.org/F4320321800","funder_display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek"}],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7130430203.pdf","grobid_xml":"https://content.openalex.org/works/W7130430203.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W114979488","https://openalex.org/W1973013779","https://openalex.org/W2011979623","https://openalex.org/W2016140364","https://openalex.org/W2025017159","https://openalex.org/W2035309264","https://openalex.org/W2039867272","https://openalex.org/W2066459185","https://openalex.org/W2109080678","https://openalex.org/W2157202548","https://openalex.org/W2228126549","https://openalex.org/W2487779201","https://openalex.org/W2493389545","https://openalex.org/W2618575259","https://openalex.org/W2903337614","https://openalex.org/W3045568673","https://openalex.org/W3119019335","https://openalex.org/W4214690803","https://openalex.org/W4240790602","https://openalex.org/W4297614128","https://openalex.org/W4313165360","https://openalex.org/W4385444334","https://openalex.org/W4391020455","https://openalex.org/W4415293176"],"related_works":[],"abstract_inverted_index":{"Abstract":[0],"We":[1,160,173],"compensate":[2],"for":[3,58,87],"the":[4,17,77,88,93,99,112,144,148,155,158,171,176],"scalability":[5],"issues":[6],"in":[7,63,154],"controller":[8,57,84,95,101,178],"synthesis":[9],"by":[10],"developing":[11],"a":[12,38,49,56,59,73,83,166,183],"hierarchical":[13,65],"control":[14],"scheme":[15,54],"within":[16],"framework":[18],"of":[19,48,76,114,147,157],"(":[20,115],"$$\\upgamma":[21,116],",\\updelta":[22,117],"$$":[23,118],"<mml:math":[24,119,133],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[25,120,134],"<mml:mrow>":[26,121],"<mml:mi>\u03b3</mml:mi>":[27,122],"<mml:mo>,</mml:mo>":[28,123],"<mml:mi>\u03b4</mml:mi>":[29,124],"</mml:mrow>":[30,125],"</mml:math>":[31,126,139],")-similarity,":[32],"which":[33,71],"measures":[34],"to":[35,142,164,169],"what":[36],"extent":[37],"potentially":[39],"non-deterministic":[40,60],"system":[41,62,150],"satisfies":[42],"specifications":[43],"expressed":[44],"as":[45],"solution":[46],"trajectories":[47],"dynamical":[50],"\u2018specification\u2019":[51],"system.":[52,90],"This":[53],"synthesizes":[55],"\u2018concrete\u2019":[61],"three":[64],"steps.":[66],"First,":[67],"an":[68,103,130],"\u2018abstract\u2019":[69],"system,":[70,79],"is":[72,80,85,96],"low-dimensional":[74],"model":[75],"concrete":[78,100,149,184],"obtained.":[81],"Then,":[82],"designed":[86],"abstract":[89,94,177],"At":[91],"last,":[92],"refined":[97],"into":[98,182],"through":[102],"\u2018interface\u2019.":[104],"To":[105],"enable":[106],"this,":[107],"we":[108],"introduce":[109],"and":[110,151,179],"characterize":[111],"notion":[113],")-abstraction":[127],"that":[128],"utilizes":[129],"$$\\mathcal":[131],"{L}_2$$":[132],"<mml:msub>":[135],"<mml:mi>L</mml:mi>":[136],"<mml:mn>2</mml:mn>":[137],"</mml:msub>":[138],"approximation":[140],"metric":[141],"measure":[143],"behavioral":[145],"similarity":[146],"its":[152],"abstraction":[153],"presence":[156],"interface.":[159,172],"utilize":[161],"this":[162],"characterization":[163],"propose":[165],"step-by-step":[167],"procedure":[168],"construct":[170],"then":[174],"synthesize":[175],"refine":[180],"it":[181],"one.":[185]},"counts_by_year":[],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2026-02-19T00:00:00"}