{"id":"https://openalex.org/W3018936306","doi":"https://doi.org/10.1109/cdc42340.2020.9304079","title":"Two-Level Lattice Neural Network Architectures for Control of Nonlinear Systems","display_name":"Two-Level Lattice Neural Network Architectures for Control of Nonlinear Systems","publication_year":2020,"publication_date":"2020-12-14","ids":{"openalex":"https://openalex.org/W3018936306","doi":"https://doi.org/10.1109/cdc42340.2020.9304079","mag":"3018936306"},"language":"en","primary_location":{"id":"doi:10.1109/cdc42340.2020.9304079","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc42340.2020.9304079","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 59th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2004.09628","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067988882","display_name":"James Ferlez","orcid":"https://orcid.org/0000-0002-1872-6315"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"James Ferlez","raw_affiliation_strings":["University of California, Irvine","University of California, Irvine **"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Irvine","institution_ids":["https://openalex.org/I204250578"]},{"raw_affiliation_string":"University of California, Irvine **","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103171121","display_name":"Xiaowu Sun","orcid":"https://orcid.org/0000-0002-9216-0866"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaowu Sun","raw_affiliation_strings":["University of California, Irvine","University of California, Irvine **"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Irvine","institution_ids":["https://openalex.org/I204250578"]},{"raw_affiliation_string":"University of California, Irvine **","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019844918","display_name":"Yasser Shoukry","orcid":"https://orcid.org/0000-0002-8224-8477"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yasser Shoukry","raw_affiliation_strings":["University of California, Irvine","University of California, Irvine **"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California, Irvine","institution_ids":["https://openalex.org/I204250578"]},{"raw_affiliation_string":"University of California, Irvine **","institution_ids":["https://openalex.org/I204250578"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I204250578"],"apc_list":null,"apc_paid":null,"fwci":0.5749,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6833434,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"2198","last_page":"2203"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9994999766349792,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9962000250816345,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9919000267982483,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.8035153746604919},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5868523716926575},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.5478184223175049},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5247326493263245},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5117866396903992},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.474112331867218},{"id":"https://openalex.org/keywords/lattice","display_name":"Lattice (music)","score":0.4593750238418579},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.44884783029556274},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.4452555775642395},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.4281467795372009},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4063677191734314},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.33001473546028137},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3292704224586487},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.19455796480178833},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.14535829424858093},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.14272066950798035},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11418846249580383}],"concepts":[{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.8035153746604919},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5868523716926575},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.5478184223175049},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5247326493263245},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5117866396903992},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.474112331867218},{"id":"https://openalex.org/C2781204021","wikidata":"https://www.wikidata.org/wiki/Q6497091","display_name":"Lattice (music)","level":2,"score":0.4593750238418579},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.44884783029556274},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.4452555775642395},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.4281467795372009},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4063677191734314},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.33001473546028137},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3292704224586487},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.19455796480178833},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.14535829424858093},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.14272066950798035},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11418846249580383},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1109/cdc42340.2020.9304079","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc42340.2020.9304079","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2020 59th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2004.09628","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.09628","pdf_url":"https://arxiv.org/pdf/2004.09628","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3018936306","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2004.09628.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:escholarship.org/ark:/13030/qt6f85x9k6","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/6f85x9k6","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"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":"","raw_type":"article"},{"id":"doi:10.48550/arxiv.2004.09628","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2004.09628","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2004.09628","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2004.09628","pdf_url":"https://arxiv.org/pdf/2004.09628","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3018936306.pdf","grobid_xml":"https://content.openalex.org/works/W3018936306.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1483893502","https://openalex.org/W1565544898","https://openalex.org/W2079042739","https://openalex.org/W2097998348","https://openalex.org/W2169289043","https://openalex.org/W2270245739","https://openalex.org/W2342840547","https://openalex.org/W2487779201","https://openalex.org/W2561773129","https://openalex.org/W2899457449","https://openalex.org/W2913773024","https://openalex.org/W2951886768","https://openalex.org/W3009132161","https://openalex.org/W3021407934","https://openalex.org/W3045568673","https://openalex.org/W3120936110","https://openalex.org/W6674385629","https://openalex.org/W6693919493","https://openalex.org/W6704559304","https://openalex.org/W6729972426","https://openalex.org/W6758982903"],"related_works":["https://openalex.org/W3120936110","https://openalex.org/W3021407934","https://openalex.org/W3132132679","https://openalex.org/W3196900140","https://openalex.org/W3202816128","https://openalex.org/W2626298162","https://openalex.org/W3019797405","https://openalex.org/W2791251367","https://openalex.org/W3135195117","https://openalex.org/W2953707919","https://openalex.org/W2887532679","https://openalex.org/W1808217111","https://openalex.org/W2810195925","https://openalex.org/W2128833259","https://openalex.org/W3120012985","https://openalex.org/W2899168325","https://openalex.org/W2189161041","https://openalex.org/W3040825053","https://openalex.org/W2068949505","https://openalex.org/W3010045995"],"abstract_inverted_index":{"In":[0],"this":[1,129],"paper,":[2],"we":[3,74,101,131,155],"consider":[4],"the":[5,29,65,79,104,133,150,157,162,180,187],"problem":[6],"of":[7,20,24,64,135,182],"automatically":[8],"designing":[9,198],"a":[10,38,61,72,76,87,110,124,141,168,199],"Rectified":[11],"Linear":[12],"Unit":[13],"(ReLU)":[14],"Neural":[15],"Network":[16],"(NN)":[17],"architecture":[18,82,171,201],"(number":[19],"layers":[21],"and":[22],"number":[23,134,181],"neurons":[25],"per":[26],"layer)":[27],"with":[28],"guarantee":[30,77],"that":[31,78,89,103,114,147,172,185],"it":[32,190],"is":[33,83,115,121],"sufficiently":[34],"parametrized":[35],"to":[36,53,67,85,139,175,202],"control":[37,203],"nonlinear":[39],"system.":[40],"Whereas":[41],"current":[42],"state-of-the-art":[43],"techniques":[44],"are":[45],"based":[46],"on":[47,161],"hand-picked":[48],"architectures":[49],"or":[50],"heuristic-based":[51],"search":[52],"find":[54],"such":[55],"NN":[56,81,166,170,200],"architectures,":[57],"our":[58,195],"approach":[59,95],"exploits":[60,96],"given":[62],"model":[63],"system":[66,105],"design":[68],"an":[69,91,204],"architecture;":[70],"as":[71],"result,":[73],"provide":[75],"resulting":[80],"sufficient":[84],"implement":[86],"controller":[88,113],"satisfies":[90],"achievable":[92],"specification.":[93],"Our":[94],"two":[97],"basic":[98],"ideas.":[99],"First,":[100],"assume":[102],"can":[106,148],"be":[107,176],"controlled":[108],"by":[109,123,179,197],"Lipschitz-continuous":[111,152],"state-feedback":[112],"unknown":[116,151],"but":[117],"whose":[118],"Lipschitz":[119],"constant":[120],"upper-bounded":[122],"known":[125],"constant;":[126],"then":[127],"using":[128],"assumption,":[130],"bound":[132],"affine":[136,183],"functions":[137,184],"needed":[138],"construct":[140],"Continuous":[142],"Piecewise":[143],"Affine":[144],"(CPWA)":[145],"function":[146,189],"approximate":[149],"controller.":[153],"Second,":[154],"utilize":[156],"authors'":[158],"recent":[159],"results":[160],"Two-Level":[163],"Lattice":[164],"(TLL)":[165],"architecture,":[167],"novel":[169],"was":[173],"shown":[174],"parameterized":[177],"directly":[178],"comprise":[186],"CPWA":[188],"realizes.":[191],"We":[192],"also":[193],"evaluate":[194],"method":[196],"inverted":[205],"pendulum.":[206]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3}],"updated_date":"2026-08-05T07:39:15.569665","created_date":"2025-10-10T00:00:00"}