{"id":"https://openalex.org/W1529039533","doi":"https://doi.org/10.1109/acc.2015.7171069","title":"A variational derivation of LQR for piecewise time-varying systems","display_name":"A variational derivation of LQR for piecewise time-varying systems","publication_year":2015,"publication_date":"2015-07-01","ids":{"openalex":"https://openalex.org/W1529039533","doi":"https://doi.org/10.1109/acc.2015.7171069","mag":"1529039533"},"language":"en","primary_location":{"id":"doi:10.1109/acc.2015.7171069","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7171069","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5074796509","display_name":"Alex Ansari","orcid":null},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Alex Ansari","raw_affiliation_strings":["Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","Department of Mechanical Engineering, McCormick School of Engineering and Applied Science, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Department of Mechanical Engineering, McCormick School of Engineering and Applied Science, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067725461","display_name":"Todd D. Murphey","orcid":"https://orcid.org/0000-0003-2262-8176"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Todd Murphey","raw_affiliation_strings":["Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","Department of Mechanical Engineering, McCormick School of Engineering and Applied Science, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Department of Mechanical Engineering, McCormick School of Engineering and Applied Science, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA","institution_ids":["https://openalex.org/I111979921"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"3","issue":null,"first_page":"2260","last_page":"2265"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9977999925613403,"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":0.9977999925613403,"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/T10040","display_name":"Adaptive Control of Nonlinear Systems","score":0.9934999942779541,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.992900013923645,"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/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.8795435428619385},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.724087119102478},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7134861946105957},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.6871272921562195},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.657126784324646},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.46835440397262573},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4564431309700012},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4336867928504944},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3552817106246948},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2229098677635193},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1863022744655609},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.15550470352172852}],"concepts":[{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.8795435428619385},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.724087119102478},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7134861946105957},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.6871272921562195},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.657126784324646},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.46835440397262573},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4564431309700012},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4336867928504944},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3552817106246948},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2229098677635193},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1863022744655609},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.15550470352172852},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/acc.2015.7171069","is_oa":false,"landing_page_url":"https://doi.org/10.1109/acc.2015.7171069","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 American Control Conference (ACC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.550000011920929,"display_name":"Quality Education","id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337391","display_name":"Division of Civil, Mechanical and Manufacturing Innovation","ror":"https://ror.org/028yd4c30"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W177930832","https://openalex.org/W287703190","https://openalex.org/W619764434","https://openalex.org/W1522531528","https://openalex.org/W1561307122","https://openalex.org/W1578936488","https://openalex.org/W1999484566","https://openalex.org/W2027701333","https://openalex.org/W2066557929","https://openalex.org/W2083402998","https://openalex.org/W2104128408","https://openalex.org/W2105934661","https://openalex.org/W2134935236","https://openalex.org/W2334591577","https://openalex.org/W2341171179","https://openalex.org/W2559873059","https://openalex.org/W3035578948","https://openalex.org/W4250589301","https://openalex.org/W4301747304","https://openalex.org/W6610258161","https://openalex.org/W6619272720","https://openalex.org/W6650404023","https://openalex.org/W6704298589","https://openalex.org/W6780383567"],"related_works":["https://openalex.org/W4239477580","https://openalex.org/W4255265352","https://openalex.org/W2921905705","https://openalex.org/W1632524629","https://openalex.org/W2902017027","https://openalex.org/W2110376385","https://openalex.org/W2766998270","https://openalex.org/W2950982235","https://openalex.org/W2052286527","https://openalex.org/W4306892756"],"abstract_inverted_index":{"This":[0],"paper":[1,113],"provides":[2,57],"a":[3,58],"complete":[4],"derivation":[5,26,91],"for":[6],"LQR":[7],"optimal":[8,12,78,86],"controllers":[9],"and":[10,63,72,81,117],"the":[11,25,31,40,51,69,85,90,101,109],"value":[13,87],"function":[14],"using":[15],"basic":[16],"principles":[17],"from":[18],"variational":[19],"calculus.":[20],"As":[21,106],"opposed":[22],"to":[23,84,115],"alternatives,":[24],"does":[27],"not":[28],"rely":[29],"on":[30],"Hamilton-Jacobi-Bellman":[32],"(HJB)":[33],"equations,":[34],"Pontryagin's":[35],"Maximum":[36],"Principle":[37],"(PMP),":[38],"or":[39,103],"Euler":[41],"Lagrange":[42],"(EL)":[43],"equations.":[44,105],"Because":[45],"it":[46],"requires":[47,93],"significantly":[48],"less":[49],"background,":[50],"approach":[52],"is":[53],"educationally":[54],"instructive.":[55],"It":[56],"different":[59],"perspective":[60],"of":[61],"how":[62],"why":[64],"key":[65],"quantities":[66],"such":[67],"as":[68],"adjoint":[70],"variable":[71],"Riccati":[73],"equation":[74],"show":[75],"up":[76],"in":[77,99,111,123],"control":[79],"computations":[80],"their":[82],"connection":[83],"function.":[88],"Additionally,":[89],"presented":[92],"fewer":[94],"regularity":[95],"assumptions":[96],"than":[97],"necessary":[98],"applying":[100],"HJB":[102],"EL":[104],"with":[107],"PMP,":[108],"methods":[110],"this":[112],"apply":[114],"systems":[116],"controls":[118],"that":[119],"are":[120],"piecewise":[121],"continuous":[122],"time.":[124]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
