{"id":"https://openalex.org/W4382935777","doi":"https://doi.org/10.23919/acc55779.2023.10156062","title":"A Reduced Order Iterative Linear Quadratic Regulator (ILQR) Technique for the Optimal Control of Nonlinear Partial Differential Equations","display_name":"A Reduced Order Iterative Linear Quadratic Regulator (ILQR) Technique for the Optimal Control of Nonlinear Partial Differential Equations","publication_year":2023,"publication_date":"2023-05-31","ids":{"openalex":"https://openalex.org/W4382935777","doi":"https://doi.org/10.23919/acc55779.2023.10156062"},"language":"en","primary_location":{"id":"doi:10.23919/acc55779.2023.10156062","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc55779.2023.10156062","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 American Control Conference (ACC)","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/A5078202724","display_name":"Aayushman Sharma","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Aayushman Sharma","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061286389","display_name":"Suman Chakravorty","orcid":"https://orcid.org/0000-0003-3074-3406"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Suman Chakravorty","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5859,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.62801592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"3389","last_page":"3394"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9983000159263611,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9983000159263611,"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/T11749","display_name":"Iterative Learning Control Systems","score":0.9972000122070312,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.7247757315635681},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6598436832427979},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6219881176948547},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.6152657270431519},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5917713642120361},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5897493362426758},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5796381235122681},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5395208597183228},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5340750217437744},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5313171744346619},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.49609002470970154},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.47378039360046387},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.43544524908065796},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.405592679977417},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2816363275051117},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20757463574409485},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.10091078281402588},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08415302634239197}],"concepts":[{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.7247757315635681},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6598436832427979},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6219881176948547},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.6152657270431519},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5917713642120361},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5897493362426758},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5796381235122681},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5395208597183228},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5340750217437744},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5313171744346619},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.49609002470970154},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.47378039360046387},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.43544524908065796},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.405592679977417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2816363275051117},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20757463574409485},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.10091078281402588},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08415302634239197},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/acc55779.2023.10156062","is_oa":false,"landing_page_url":"https://doi.org/10.23919/acc55779.2023.10156062","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2023 American Control Conference (ACC)","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":20,"referenced_works":["https://openalex.org/W195033972","https://openalex.org/W1624426313","https://openalex.org/W1633869374","https://openalex.org/W2001027221","https://openalex.org/W2021135119","https://openalex.org/W2041001120","https://openalex.org/W2046528357","https://openalex.org/W2064733273","https://openalex.org/W2140820418","https://openalex.org/W2239232218","https://openalex.org/W2527640678","https://openalex.org/W2581292955","https://openalex.org/W2986527241","https://openalex.org/W3012408196","https://openalex.org/W3184053186","https://openalex.org/W4210250498","https://openalex.org/W4213063365","https://openalex.org/W4237591687","https://openalex.org/W6607786297","https://openalex.org/W7043020910"],"related_works":["https://openalex.org/W3103325625","https://openalex.org/W1486898455","https://openalex.org/W2041905724","https://openalex.org/W4311726894","https://openalex.org/W2991463004","https://openalex.org/W2088588293","https://openalex.org/W2949122357","https://openalex.org/W3090727460","https://openalex.org/W2203843426","https://openalex.org/W2049369111"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"introduce":[4],"a":[5,27,42,56,70,88,123],"reduced":[6,43,73,90],"order":[7,44,74],"Iterative":[8],"Linear":[9,45],"Quadratic":[10],"Regulator":[11],"(RO-ILQR)":[12],"approach":[13,25,98],"for":[14,111],"the":[15,31,36,51,60,64,83,102,117,127,131],"optimal":[16,61,84],"control":[17],"of":[18,30,38,50,59,82],"nonlinear":[19,52],"Partial":[20],"Differential":[21],"Equations":[22],"(PDE).":[23],"The":[24,96],"proposes":[26],"novel":[28],"modification":[29],"ILQR":[32,133],"technique:":[33],"it":[34],"uses":[35],"Method":[37],"Snapshots":[39],"to":[40,68,77],"identify":[41],"Time":[46],"Varying":[47],"(LTV)":[48],"approximation":[49],"PDE":[53],"dynamics":[54],"around":[55],"current":[57],"estimate":[58,81],"trajectory,":[62],"utilizes":[63],"identified":[65],"LTV":[66],"model":[67],"solve":[69],"time":[71],"varying":[72],"LQR":[75],"problem":[76],"obtain":[78],"an":[79],"improved":[80],"trajectory":[85],"along":[86],"with":[87],"new":[89],"basis,":[91],"and":[92,106,116],"iterates":[93],"till":[94],"convergence.":[95],"proposed":[97],"is":[99,122],"tested":[100],"on":[101],"viscous":[103],"Burger\u2019s":[104],"equation":[105],"two":[107],"phase":[108],"field":[109],"models":[110],"microstructure":[112],"evolution":[113],"in":[114,126],"materials,":[115],"results":[118],"show":[119],"that":[120],"there":[121],"significant":[124],"reduction":[125],"computational":[128],"burden":[129],"over":[130],"standard":[132],"approach,":[134],"without":[135],"sacrificing":[136],"performance.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
