{"id":"https://openalex.org/W2038506769","doi":"https://doi.org/10.1109/cdc.2013.6761114","title":"A fast condensing method for solution of linear-quadratic control problems","display_name":"A fast condensing method for solution of linear-quadratic control problems","publication_year":2013,"publication_date":"2013-12-01","ids":{"openalex":"https://openalex.org/W2038506769","doi":"https://doi.org/10.1109/cdc.2013.6761114","mag":"2038506769"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2013.6761114","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6761114","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","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/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]},{"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":"Gianluca Frison","raw_affiliation_strings":["DTU Compute - Department of Applied Mathematics and Computer Science, Technical University of Denmark, Denmark","DTU Compute - Dept. of Appl. Math. & Comput. Sci., Tech. Univ. of Denmark, Lyngby, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DTU Compute - Department of Applied Mathematics and Computer Science, Technical University of Denmark, Denmark","institution_ids":["https://openalex.org/I96673099"]},{"raw_affiliation_string":"DTU Compute - Dept. of Appl. Math. & Comput. Sci., Tech. Univ. of Denmark, Lyngby, Denmark","institution_ids":["https://openalex.org/I124055696"]}]},{"author_position":"last","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/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]}],"countries":["DK"],"is_corresponding":false,"raw_author_name":"John Bagterp Jorgensen","raw_affiliation_strings":["DTU Compute - Dept. of Appl. Math. & Comput. Sci., Tech. Univ. of Denmark, Lyngby, Denmark"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"DTU Compute - Dept. of Appl. Math. & Comput. Sci., Tech. Univ. of Denmark, Lyngby, Denmark","institution_ids":["https://openalex.org/I124055696"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.5812,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.94375859,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"7715","last_page":"7720"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10791","display_name":"Advanced Control Systems Optimization","score":0.9998999834060669,"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":0.9998999834060669,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9975000023841858,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9932000041007996,"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/recursion","display_name":"Recursion (computer science)","score":0.7556478977203369},{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7317564487457275},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6579001545906067},{"id":"https://openalex.org/keywords/factorization","display_name":"Factorization","score":0.5466046333312988},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.5458640456199646},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.5323014259338379},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.513114333152771},{"id":"https://openalex.org/keywords/model-predictive-control","display_name":"Model predictive control","score":0.49823880195617676},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4763662815093994},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.47213464975357056},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.46759480237960815},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4592994749546051},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43637365102767944},{"id":"https://openalex.org/keywords/computational-problem","display_name":"Computational problem","score":0.4299989342689514},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4243106544017792},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42222777009010315},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.340782105922699},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3158223032951355},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.20839864015579224}],"concepts":[{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.7556478977203369},{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7317564487457275},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6579001545906067},{"id":"https://openalex.org/C187834632","wikidata":"https://www.wikidata.org/wiki/Q188804","display_name":"Factorization","level":2,"score":0.5466046333312988},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.5458640456199646},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.5323014259338379},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.513114333152771},{"id":"https://openalex.org/C172205157","wikidata":"https://www.wikidata.org/wiki/Q1782962","display_name":"Model predictive control","level":3,"score":0.49823880195617676},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4763662815093994},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.47213464975357056},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.46759480237960815},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4592994749546051},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43637365102767944},{"id":"https://openalex.org/C19754495","wikidata":"https://www.wikidata.org/wiki/Q3435924","display_name":"Computational problem","level":2,"score":0.4299989342689514},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4243106544017792},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42222777009010315},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.340782105922699},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3158223032951355},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.20839864015579224},{"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/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/cdc.2013.6761114","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2013.6761114","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"52nd IEEE Conference on Decision and Control","raw_type":"proceedings-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.728.4132","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.728.4132","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www2.imm.dtu.dk/%7Egiaf/giaf_cdc13.pdf","raw_type":"text"},{"id":"pmh:oai:pure.atira.dk:publications/2a528106-c9b5-45a8-a892-05b3ad63f7f1","is_oa":false,"landing_page_url":"https://orbit.dtu.dk/en/publications/2a528106-c9b5-45a8-a892-05b3ad63f7f1","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 & J\u00f8rgensen , J B 2013 , A Fast Condensing Method for Solution of Linear-Quadratic Control Problems . in 52nd IEEE Conference on Decision and Control . IEEE , pp. 7715-7720 , 52nd IEEE Conference on Decision and Control (CDC 2013) , Florence , Italy , 10/12/2013 . https://doi.org/10.1109/CDC.2013.6761114","raw_type":"contributionToPeriodical"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W201964146","https://openalex.org/W1603657390","https://openalex.org/W2024321257","https://openalex.org/W2045448539","https://openalex.org/W2075055460","https://openalex.org/W2613558549","https://openalex.org/W4293775970"],"related_works":["https://openalex.org/W2611031068","https://openalex.org/W1704347466","https://openalex.org/W4283017538","https://openalex.org/W1996936972","https://openalex.org/W1545275724","https://openalex.org/W2802707792","https://openalex.org/W2075777916","https://openalex.org/W3021699548","https://openalex.org/W2569979269","https://openalex.org/W4291718021"],"abstract_inverted_index":{"In":[0,40],"both":[1,73],"Active-Set":[2],"(AS)":[3],"and":[4,61,79,101,114],"Interior-Point":[5],"(IP)":[6],"algorithms":[7],"for":[8],"Model":[9],"Predictive":[10],"Control":[11],"(MPC),":[12],"sub-problems":[13,33],"in":[14,109,116,131],"the":[15,36,57,67,75,81,96,110,117,132,139,144,154],"form":[16],"of":[17,31,56,69,119,141],"linear-quadratic":[18],"(LQ)":[19],"control":[20,59,111,133],"problems":[21],"need":[22],"to":[23,51,65,72,95],"be":[24],"solved":[25],"at":[26],"each":[27],"iteration.":[28],"The":[29,89,121],"solution":[30],"these":[32],"is":[34,92,107,129,147,151],"usually":[35],"main":[37],"computational":[38,104,126],"effort.":[39],"this":[41,70,149],"paper":[42],"we":[43,62,84],"consider":[44],"a":[45,103,125],"condensing":[46],"(or":[47],"state":[48,145],"elimination)":[49],"method":[50],"solve":[52,80],"an":[53],"extended":[54],"version":[55],"LQ":[58],"problem,":[60],"show":[63],"how":[64],"exploit":[66],"structure":[68],"problem":[71],"factorize":[74],"dense":[76],"Hessian":[77],"matrix":[78],"system.":[82],"Furthermore,":[83],"present":[85],"two":[86],"efficient":[87],"implementations.":[88],"first":[90],"implementation":[91,123,150],"formally":[93],"identical":[94],"Riccati":[97,155],"recursion":[98,156],"based":[99,157],"solver":[100],"has":[102,124],"complexity":[105,127],"that":[106,128],"linear":[108],"horizon":[112,134],"length":[113,135],"cubic":[115],"number":[118,140],"states.":[120,142],"second":[122],"quadratic":[130],"as":[136,138],"well":[137],"When":[143],"dimension":[146],"high,":[148],"faster":[152],"than":[153],"implementation.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}