{"id":"https://openalex.org/W2569940025","doi":"https://doi.org/10.1109/cdc.2016.7798946","title":"An efficient implementation of partial condensing for Nonlinear Model Predictive Control","display_name":"An efficient implementation of partial condensing for Nonlinear Model Predictive Control","publication_year":2016,"publication_date":"2016-12-01","ids":{"openalex":"https://openalex.org/W2569940025","doi":"https://doi.org/10.1109/cdc.2016.7798946","mag":"2569940025"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2016.7798946","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798946","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th 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/A5038053055","display_name":"Gianluca Frison","orcid":"https://orcid.org/0000-0001-9440-9699"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]},{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]},{"id":"https://openalex.org/I4210153877","display_name":"Microsystems (United Kingdom)","ror":"https://ror.org/04pvywd96","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210153877"]}],"countries":["DE","DK","GB"],"is_corresponding":true,"raw_author_name":"Gianluca Frison","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Technical University of Denmark","Department of Microsystems Engineering, University of Freiburg"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Technical University of Denmark","institution_ids":["https://openalex.org/I96673099"]},{"raw_affiliation_string":"Department of Microsystems Engineering, University of Freiburg","institution_ids":["https://openalex.org/I161046081","https://openalex.org/I4210153877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063456024","display_name":"Dimitris Kouzoupis","orcid":"https://orcid.org/0000-0002-5772-8276"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]},{"id":"https://openalex.org/I4210153877","display_name":"Microsystems (United Kingdom)","ror":"https://ror.org/04pvywd96","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210153877"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Dimitris Kouzoupis","raw_affiliation_strings":["Department of Microsystems Engineering, University of Freiburg"],"affiliations":[{"raw_affiliation_string":"Department of Microsystems Engineering, University of Freiburg","institution_ids":["https://openalex.org/I161046081","https://openalex.org/I4210153877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050946774","display_name":"John Bagterp J\u00f8rgensen","orcid":"https://orcid.org/0000-0001-9799-2808"},"institutions":[{"id":"https://openalex.org/I96673099","display_name":"Technical University of Denmark","ror":"https://ror.org/04qtj9h94","country_code":"DK","type":"education","lineage":["https://openalex.org/I96673099"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"John Bagterp Jorgensen","raw_affiliation_strings":["Department of Applied Mathematics and Computer Science, Technical University of Denmark"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Computer Science, Technical University of Denmark","institution_ids":["https://openalex.org/I96673099"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057375078","display_name":"Moritz Diehl","orcid":"https://orcid.org/0000-0001-6556-8252"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]},{"id":"https://openalex.org/I4210153877","display_name":"Microsystems (United Kingdom)","ror":"https://ror.org/04pvywd96","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210153877"]}],"countries":["DE","GB"],"is_corresponding":false,"raw_author_name":"Moritz Diehl","raw_affiliation_strings":["Department of Microsystems Engineering, University of Freiburg"],"affiliations":[{"raw_affiliation_string":"Department of Microsystems Engineering, University of Freiburg","institution_ids":["https://openalex.org/I161046081","https://openalex.org/I4210153877"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5038053055"],"corresponding_institution_ids":["https://openalex.org/I161046081","https://openalex.org/I4210153877","https://openalex.org/I96673099"],"apc_list":null,"apc_paid":null,"fwci":2.7081,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.90950714,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"4457","last_page":"4462"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9995999932289124,"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":0.9995999932289124,"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/T10409","display_name":"Fuel Cells and Related Materials","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9889000058174133,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.6973676085472107},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6509997844696045},{"id":"https://openalex.org/keywords/model-predictive-control","display_name":"Model predictive control","score":0.6316401958465576},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5384175181388855},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5240347981452942},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4872514307498932},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.48258984088897705},{"id":"https://openalex.org/keywords/benchmarking","display_name":"Benchmarking","score":0.48104313015937805},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.43978869915008545},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3634427785873413},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3160053491592407},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.24678251147270203},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.18914112448692322},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12242531776428223}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.6973676085472107},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6509997844696045},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.6316401958465576},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5384175181388855},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5240347981452942},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4872514307498932},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.48258984088897705},{"id":"https://openalex.org/C86251818","wikidata":"https://www.wikidata.org/wiki/Q816754","display_name":"Benchmarking","level":2,"score":0.48104313015937805},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.43978869915008545},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3634427785873413},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3160053491592407},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.24678251147270203},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.18914112448692322},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12242531776428223},{"id":"https://openalex.org/C162853370","wikidata":"https://www.wikidata.org/wiki/Q39809","display_name":"Marketing","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2016.7798946","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2016.7798946","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2016 IEEE 55th Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.atira.dk:publications/b4ff355f-dbd2-4c49-9490-9875d6662143","is_oa":false,"landing_page_url":"https://orbit.dtu.dk/en/publications/b4ff355f-dbd2-4c49-9490-9875d6662143","pdf_url":null,"source":{"id":"https://openalex.org/S4306400705","display_name":"Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I96673099","host_organization_name":"Technical University of Denmark","host_organization_lineage":["https://openalex.org/I96673099"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Frison , G , Kouzoupis , D , J\u00f8rgensen , J B &amp; Diehl , M 2016 , An Efficient Implementation of Partial Condensing for Nonlinear Model Predictive Control . in Proceedings of the 55th IEEE Conference on Decision and Control (CDC 2016) . IEEE , pp. 4457-4462 , 55th IEEE Conference on Decision and Control , Las Vegas , United States , 12/12/2016 . https://doi.org/10.1109/CDC.2016.7798946","raw_type":"contributionToPeriodical"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.5099999904632568}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W201964146","https://openalex.org/W1545385270","https://openalex.org/W1603657390","https://openalex.org/W1971930153","https://openalex.org/W2016331189","https://openalex.org/W2024321257","https://openalex.org/W2026079951","https://openalex.org/W2038506769","https://openalex.org/W2070576018","https://openalex.org/W2075055460","https://openalex.org/W2116901509","https://openalex.org/W2323956929","https://openalex.org/W2399393671","https://openalex.org/W2550341318","https://openalex.org/W2595724041","https://openalex.org/W2613558549"],"related_works":["https://openalex.org/W4238897586","https://openalex.org/W435179959","https://openalex.org/W2619091065","https://openalex.org/W2059640416","https://openalex.org/W2080896647","https://openalex.org/W2025587901","https://openalex.org/W2028217664","https://openalex.org/W2158000646","https://openalex.org/W2886734572","https://openalex.org/W1852236601"],"abstract_inverted_index":{"Partial":[0,127],"(or":[1],"block)":[2],"condensing":[3,62,128,163],"is":[4,74,93],"a":[5,11,18,60,71,96,124,134],"recently":[6],"proposed":[7],"technique":[8,135],"to":[9,45,136],"reformulate":[10],"Model":[12],"Predictive":[13],"Control":[14],"(MPC)":[15],"problem":[16,49],"into":[17],"form":[19],"more":[20],"suitable":[21],"for":[22,33,51,67,119],"structure-exploiting":[23],"Quadratic":[24],"Programming":[25],"(QP)":[26],"solvers.":[27],"It":[28],"trades":[29],"off":[30],"horizon":[31],"length":[32],"input":[34],"vector":[35],"size,":[36],"and":[37],"this":[38],"degree":[39],"of":[40,83,99,115,158],"freedom":[41],"can":[42,129,164],"be":[43,131],"employed":[44],"find":[46],"the":[47,52,84,113,169],"best":[48],"size":[50],"QP":[53],"solver":[54],"at":[55,80],"hand.":[56],"This":[57],"paper":[58],"proposes":[59],"Hessian":[61],"algorithm":[63],"particularly":[64],"well":[65,107],"suited":[66],"partial":[68,162],"condensing,":[69],"where":[70,149],"state":[72],"component":[73],"retained":[75],"as":[76,106,108,133],"an":[77],"optimization":[78],"variable":[79],"each":[81],"stage":[82],"partially":[85],"condensed":[86],"MPC":[87,160],"problem.":[88],"The":[89],"optimal":[90],"input-horizon":[91],"trade-off":[92],"investigated":[94],"from":[95],"theoretical":[97],"point":[98],"view":[100],"(based":[101],"on":[102,140,146],"algorithms":[103],"flop":[104,170],"count)":[105],"by":[109],"benchmarking":[110],"(in":[111],"practice,":[112],"performance":[114,167],"linear":[116,150],"algebra":[117,151],"routines":[118,152],"different":[120],"matrix":[121],"sizes":[122],"plays":[123],"key":[125],"role).":[126],"also":[130],"seen":[132],"replace":[137],"many":[138],"operations":[139,145],"small":[141],"matrices":[142],"with":[143],"fewer":[144],"larger":[147],"matrices,":[148],"perform":[153],"better.":[154],"Therefore,":[155],"in":[156],"case":[157],"small-scale":[159],"problems,":[161],"greatly":[165],"improve":[166],"beyond":[168],"count":[171],"reduction.":[172]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
