{"id":"https://openalex.org/W2076199517","doi":"https://doi.org/10.1109/tac.2016.2562062","title":"Convex Relaxation for Optimal Distributed Control Problems","display_name":"Convex Relaxation for Optimal Distributed Control Problems","publication_year":2016,"publication_date":"2016-05-03","ids":{"openalex":"https://openalex.org/W2076199517","doi":"https://doi.org/10.1109/tac.2016.2562062","mag":"2076199517"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2016.2562062","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2562062","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-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/A5042586538","display_name":"Ghazal Fazelnia","orcid":"https://orcid.org/0000-0002-8833-8465"},"institutions":[{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ghazal Fazelnia","raw_affiliation_strings":["Electrical Engineering Department, Columbia University, New York, NY, USA","[Electrical Engineering Department, Columbia University, New York, NY, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, Columbia University, New York, NY, USA","institution_ids":["https://openalex.org/I78577930"]},{"raw_affiliation_string":"[Electrical Engineering Department, Columbia University, New York, NY, USA]","institution_ids":["https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015341130","display_name":"Ramtin Madani","orcid":"https://orcid.org/0000-0001-9246-2357"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ramtin Madani","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA","[Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"[Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA]","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072608035","display_name":"Abdulrahman Kalbat","orcid":"https://orcid.org/0000-0003-4615-3654"},"institutions":[{"id":"https://openalex.org/I201726411","display_name":"United Arab Emirates University","ror":"https://ror.org/01km6p862","country_code":"AE","type":"education","lineage":["https://openalex.org/I201726411"]}],"countries":["AE"],"is_corresponding":false,"raw_author_name":"Abdulrahman Kalbat","raw_affiliation_strings":["Electrical Engineering Department, United Arab Emirates University, Berkeley, CA, USA","[Electrical Engineering Department, United Arab Emirates University, Berkeley, CA, USA]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Electrical Engineering Department, United Arab Emirates University, Berkeley, CA, USA","institution_ids":["https://openalex.org/I201726411"]},{"raw_affiliation_string":"[Electrical Engineering Department, United Arab Emirates University, Berkeley, CA, USA]","institution_ids":["https://openalex.org/I201726411"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042580848","display_name":"Javad Lavaei","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Javad Lavaei","raw_affiliation_strings":["Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA","[Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA]"],"raw_orcid":"https://orcid.org/0000-0003-4294-1338","affiliations":[{"raw_affiliation_string":"Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA","institution_ids":["https://openalex.org/I95457486"]},{"raw_affiliation_string":"[Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA, USA]","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":27.6368,"has_fulltext":false,"cited_by_count":125,"citation_normalized_percentile":{"value":0.99879542,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"62","issue":"1","first_page":"206","last_page":"221"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9969000220298767,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9948999881744385,"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/relaxation","display_name":"Relaxation (psychology)","score":0.6519951820373535},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.6312054395675659},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.6169139742851257},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5961468815803528},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5610039234161377},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5596000552177429},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.5245359539985657},{"id":"https://openalex.org/keywords/linear-quadratic-gaussian-control","display_name":"Linear-quadratic-Gaussian control","score":0.5112035870552063},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.47332438826560974},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44297346472740173},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.3899502754211426},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2897701859474182},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1342281699180603},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.0679808259010315},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.06753677129745483}],"concepts":[{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6519951820373535},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6312054395675659},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.6169139742851257},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5961468815803528},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5610039234161377},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5596000552177429},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.5245359539985657},{"id":"https://openalex.org/C204495892","wikidata":"https://www.wikidata.org/wiki/Q1798304","display_name":"Linear-quadratic-Gaussian control","level":3,"score":0.5112035870552063},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.47332438826560974},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44297346472740173},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.3899502754211426},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2897701859474182},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1342281699180603},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0679808259010315},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.06753677129745483},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2016.2562062","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2016.2562062","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W1521492382","https://openalex.org/W1529743344","https://openalex.org/W1880424195","https://openalex.org/W1964527362","https://openalex.org/W1964845553","https://openalex.org/W1969729070","https://openalex.org/W1971016514","https://openalex.org/W1971390987","https://openalex.org/W1975153904","https://openalex.org/W1985123706","https://openalex.org/W1985395019","https://openalex.org/W1986347689","https://openalex.org/W1989076115","https://openalex.org/W1993446440","https://openalex.org/W2002142656","https://openalex.org/W2004936543","https://openalex.org/W2005102197","https://openalex.org/W2015089195","https://openalex.org/W2024189633","https://openalex.org/W2025621761","https://openalex.org/W2028252909","https://openalex.org/W2034902523","https://openalex.org/W2045148236","https://openalex.org/W2063046368","https://openalex.org/W2069525910","https://openalex.org/W2071143636","https://openalex.org/W2076426934","https://openalex.org/W2080362883","https://openalex.org/W2085523940","https://openalex.org/W2106424475","https://openalex.org/W2108130008","https://openalex.org/W2110540077","https://openalex.org/W2111836897","https://openalex.org/W2121154010","https://openalex.org/W2122700623","https://openalex.org/W2125430362","https://openalex.org/W2128737109","https://openalex.org/W2135519533","https://openalex.org/W2136598296","https://openalex.org/W2139833611","https://openalex.org/W2141380252","https://openalex.org/W2144784103","https://openalex.org/W2145067072","https://openalex.org/W2146223450","https://openalex.org/W2154956811","https://openalex.org/W2158983145","https://openalex.org/W2159857480","https://openalex.org/W2165894964","https://openalex.org/W2166778103","https://openalex.org/W2168209480","https://openalex.org/W2169488608","https://openalex.org/W2296319761","https://openalex.org/W2610279013","https://openalex.org/W2622952038","https://openalex.org/W2912522929","https://openalex.org/W2949975756","https://openalex.org/W2951871203","https://openalex.org/W2986773320","https://openalex.org/W3102961917","https://openalex.org/W3104452722","https://openalex.org/W4233478836","https://openalex.org/W4250589301","https://openalex.org/W4293403123","https://openalex.org/W6657043815","https://openalex.org/W6683227944","https://openalex.org/W6764519800","https://openalex.org/W7028111660"],"related_works":["https://openalex.org/W1999291921","https://openalex.org/W2107169685","https://openalex.org/W4245839115","https://openalex.org/W2111439273","https://openalex.org/W2115005925","https://openalex.org/W2101783086","https://openalex.org/W1998777431","https://openalex.org/W2619014647","https://openalex.org/W2167726841","https://openalex.org/W2047206873"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,20,32,43,88,124,136,229],"concerned":[3],"with":[4,27,35,114,139,164,175],"the":[5,63,83,91,94,120,140,148,151,179,207,225,236],"optimal":[6,34,72,172],"distributed":[7,25,73,237],"control":[8,239],"(ODC)":[9],"problem":[10,48,96,109],"for":[11,127,190,206,218],"linear":[12],"discrete-time":[13],"deterministic":[14],"and":[15,193],"stochastic":[16],"systems.":[17,242],"The":[18,185,197,222],"objective":[19,144],"to":[21,37,57,158,169],"design":[22,208],"a":[23,28,38,50,58,67,70,100,111,128,131,160,165,176,210,232],"static":[24],"controller":[26,74],"prespecified":[29],"structure":[30],"that":[31,45,90,103,142],"globally":[33,71,171],"respect":[36],"quadratic":[39,51],"cost":[40],"functional.":[41],"It":[42],"shown":[44],"this":[46,79,108,202],"NP-hard":[47],"has":[49,66,110],"formulation,":[52],"which":[53],"can":[54,75],"be":[55,76],"relaxed":[56],"semidefinite":[59],"program":[60],"(SDP).":[61],"If":[62],"SDP":[64,105,122,134,152,162,198,227],"relaxation":[65,106,123,135],"rank-1":[68,166],"solution,":[69],"recovered":[77],"from":[78],"solution.":[80,153],"By":[81],"utilizing":[82],"notion":[84],"of":[85,93,107,150,182,209,224,240],"treewidth,":[86],"it":[87],"proved":[89],"nonlinearity":[92],"ODC":[95,195],"appears":[97],"in":[98,201],"such":[99],"sparse":[101],"way":[102],"an":[104,216],"matrix":[112],"solution":[113,163],"rank":[115,149],"at":[116],"most":[117],"3.":[118],"Since":[119],"proposed":[121,157,226],"computationally":[125,132],"expensive":[126],"large-scale":[129],"system,":[130],"cheap":[133],"also":[137],"developed":[138,189,200],"property":[141],"its":[143],"function":[145],"indirectly":[146],"penalizes":[147],"Various":[154],"techniques":[155],"are":[156,188,204],"approximate":[159],"low-rank":[161],"matrix,":[167],"leading":[168],"near":[170],"controllers":[173],"together":[174],"bound":[177],"on":[178,235],"optimality":[180],"degree":[181],"each":[183],"controller.":[184],"above":[186],"results":[187],"both":[191],"finite-horizon":[192],"infinite-horizon":[194],"problems.":[196],"relaxations":[199,228],"work":[203],"exact":[205],"centralized":[211],"controller,":[212],"hence":[213],"serving":[214],"as":[215],"alternative":[217],"solving":[219],"Riccati":[220],"equations.":[221],"efficacy":[223],"elucidated":[230],"through":[231],"case":[233],"study":[234],"frequency":[238],"power":[241]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":11},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":17},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}