{"id":"https://openalex.org/W7123341179","doi":"https://doi.org/10.1109/cdc57313.2025.11312023","title":"The Bidirectional Mapping Between Linear Model Predictive Control Policies and ReLU Neural Networks","display_name":"The Bidirectional Mapping Between Linear Model Predictive Control Policies and ReLU Neural Networks","publication_year":2025,"publication_date":"2025-12-09","ids":{"openalex":"https://openalex.org/W7123341179","doi":"https://doi.org/10.1109/cdc57313.2025.11312023"},"language":null,"primary_location":{"id":"doi:10.1109/cdc57313.2025.11312023","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc57313.2025.11312023","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 64th Conference on Decision and Control (CDC)","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/A5122872650","display_name":"Xingchen Li","orcid":null},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xingchen Li","raw_affiliation_strings":["Tsinghua University,Department of Automation, and Beijing National Research Center for Info. Sci. &amp; Tech. (BNRist),Beijing,China,100084"],"affiliations":[{"raw_affiliation_string":"Tsinghua University,Department of Automation, and Beijing National Research Center for Info. Sci. &amp; Tech. (BNRist),Beijing,China,100084","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088962631","display_name":"Keyou You","orcid":"https://orcid.org/0000-0003-4355-5340"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Keyou You","raw_affiliation_strings":["Tsinghua University,Department of Automation, and Beijing National Research Center for Info. Sci. &amp; Tech. (BNRist),Beijing,China,100084"],"affiliations":[{"raw_affiliation_string":"Tsinghua University,Department of Automation, and Beijing National Research Center for Info. Sci. &amp; Tech. (BNRist),Beijing,China,100084","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5122872650"],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.64891374,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"4657","last_page":"4662"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.957099974155426,"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":0.957099974155426,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.010900000110268593,"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"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.0071000000461936,"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/artificial-neural-network","display_name":"Artificial neural network","score":0.6560999751091003},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.5332000255584717},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5327000021934509},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5048999786376953},{"id":"https://openalex.org/keywords/model-predictive-control","display_name":"Model predictive control","score":0.46869999170303345},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.4336000084877014},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.40149998664855957}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6560999751091003},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5863999724388123},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.5332000255584717},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5327000021934509},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5048999786376953},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.46869999170303345},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.4336000084877014},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.41519999504089355},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.40149998664855957},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3862000107765198},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.38260000944137573},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.36390000581741333},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35839998722076416},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3391999900341034},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.3057999908924103},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.28780001401901245},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.2833000123500824}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc57313.2025.11312023","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc57313.2025.11312023","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2025 IEEE 64th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320329860","display_name":"National Science and Technology Major Project","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Recently,":[0],"there":[1],"has":[2,38],"been":[3,40],"a":[4,46,61,91,106],"resurgence":[5],"of":[6,93,108,120,152],"interest":[7],"in":[8,26],"using":[9],"neural":[10],"networks":[11],"(NNs)":[12],"to":[13,84,148],"approximate":[14],"model":[15],"predictive":[16],"control":[17],"(MPC)":[18],"policies,":[19,88],"as":[20],"NNs":[21,37,83],"show":[22,129],"promising":[23],"computational":[24,78],"efficiency":[25],"practice.":[27],"However,":[28],"the":[29,77,117,121,150],"relation":[30],"between":[31,49],"linear":[32,138],"MPC":[33],"(LMPC)":[34],"and":[35,51],"ReLU":[36,52,62,66,82,141,158],"not":[39],"fully":[41],"studied.":[42],"This":[43],"work":[44],"establishes":[45],"bidirectional":[47],"mapping":[48],"LMPC":[50,55,73,87,131,153],"NNs:":[53],"any":[54,65,135],"policy":[56],"can":[57,68,133,156],"be":[58,69],"represented":[59,70],"by":[60,71],"NN":[63,67],"and,":[64],"an":[72],"policy.":[74],"We":[75],"analyze":[76],"complexity":[79],"required":[80],"for":[81],"exactly":[85],"represent":[86,134,157],"demonstrating":[89],"that":[90,130,155],"depth":[92,107],"\u2308log<inf":[94],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[95,97,114],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">2</inf>(n<inf":[96],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x</inf>":[98,115],"+":[99],"1)\u2309":[100],"is":[101,110,116,146],"sufficient":[102],"while":[103],"at":[104],"least":[105],"2":[109],"necessary,":[111],"where":[112],"n<inf":[113],"state":[118],"dimension":[119],"system.":[122],"Conversely,":[123],"through":[124],"explicit":[125],"constructive":[126],"proofs,":[127],"we":[128],"policies":[132,154],"continuous":[136],"piecewise":[137],"function,":[139],"including":[140],"NNs.":[142,159],"A":[143],"numerical":[144],"example":[145],"provided":[147],"illustrate":[149],"construction":[151]},"counts_by_year":[],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2026-01-14T00:00:00"}