{"id":"https://openalex.org/W1548885905","doi":"https://doi.org/10.23919/ecc.2013.6669511","title":"A max-plus based fundamental solution to a class of linear regulator problems with non-quadratic terminal payoff","display_name":"A max-plus based fundamental solution to a class of linear regulator problems with non-quadratic terminal payoff","publication_year":2013,"publication_date":"2013-07-01","ids":{"openalex":"https://openalex.org/W1548885905","doi":"https://doi.org/10.23919/ecc.2013.6669511","mag":"1548885905"},"language":"en","primary_location":{"id":"doi:10.23919/ecc.2013.6669511","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2013.6669511","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 European Control Conference (ECC)","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/A5100356931","display_name":"Huan Zhang","orcid":"https://orcid.org/0000-0001-7680-8338"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Huan Zhang","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Melbourne, Victoria, Australia","Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004101031","display_name":"Peter M. Dower","orcid":"https://orcid.org/0000-0002-9791-7776"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Peter M. Dower","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Melbourne, Victoria, Australia","Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Melbourne, Victoria, Australia","institution_ids":["https://openalex.org/I165779595"]},{"raw_affiliation_string":"Dept. of Electr. & Electron. Eng., Univ. of Melbourne, Melbourne, VIC, Australia","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100356931"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"apc_list":null,"apc_paid":null,"fwci":1.0099,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.78928731,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"2238","last_page":"2243"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9994999766349792,"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/T10046","display_name":"Stability and Control of Uncertain Systems","score":0.9994999766349792,"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":0.9965999722480774,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9951000213623047,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer 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":0.8586878776550293},{"id":"https://openalex.org/keywords/riccati-equation","display_name":"Riccati equation","score":0.6253029108047485},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6239829659461975},{"id":"https://openalex.org/keywords/linear-regulator","display_name":"Linear regulator","score":0.5752119421958923},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.5723740458488464},{"id":"https://openalex.org/keywords/stochastic-game","display_name":"Stochastic game","score":0.49904489517211914},{"id":"https://openalex.org/keywords/algebraic-riccati-equation","display_name":"Algebraic Riccati equation","score":0.49118396639823914},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4907704293727875},{"id":"https://openalex.org/keywords/terminal","display_name":"Terminal (telecommunication)","score":0.4596855342388153},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45585617423057556},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.4315551817417145},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.42402249574661255},{"id":"https://openalex.org/keywords/regulator","display_name":"Regulator","score":0.42296311259269714},{"id":"https://openalex.org/keywords/linear-programming","display_name":"Linear programming","score":0.4172448217868805},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4156755805015564},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.34288716316223145},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.27501732110977173},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.25653576850891113},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.13545647263526917},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.13397067785263062}],"concepts":[{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.8586878776550293},{"id":"https://openalex.org/C45473103","wikidata":"https://www.wikidata.org/wiki/Q851503","display_name":"Riccati equation","level":3,"score":0.6253029108047485},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6239829659461975},{"id":"https://openalex.org/C2777374959","wikidata":"https://www.wikidata.org/wiki/Q3092713","display_name":"Linear regulator","level":4,"score":0.5752119421958923},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.5723740458488464},{"id":"https://openalex.org/C22171661","wikidata":"https://www.wikidata.org/wiki/Q1074380","display_name":"Stochastic game","level":2,"score":0.49904489517211914},{"id":"https://openalex.org/C13847129","wikidata":"https://www.wikidata.org/wiki/Q4723989","display_name":"Algebraic Riccati equation","level":4,"score":0.49118396639823914},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4907704293727875},{"id":"https://openalex.org/C2779664074","wikidata":"https://www.wikidata.org/wiki/Q3518405","display_name":"Terminal (telecommunication)","level":2,"score":0.4596855342388153},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45585617423057556},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.4315551817417145},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.42402249574661255},{"id":"https://openalex.org/C6929976","wikidata":"https://www.wikidata.org/wiki/Q3771881","display_name":"Regulator","level":3,"score":0.42296311259269714},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.4172448217868805},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4156755805015564},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.34288716316223145},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.27501732110977173},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.25653576850891113},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.13545647263526917},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.13397067785263062},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.23919/ecc.2013.6669511","is_oa":false,"landing_page_url":"https://doi.org/10.23919/ecc.2013.6669511","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2013 European Control Conference (ECC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W644523282","https://openalex.org/W1522531528","https://openalex.org/W1970266193","https://openalex.org/W1991466857","https://openalex.org/W1998401686","https://openalex.org/W2008455282","https://openalex.org/W2013939926","https://openalex.org/W2017659935","https://openalex.org/W2028660300","https://openalex.org/W2059161794","https://openalex.org/W2095246006","https://openalex.org/W2106758919"],"related_works":["https://openalex.org/W2005019312","https://openalex.org/W2018296362","https://openalex.org/W2547959172","https://openalex.org/W2727200542","https://openalex.org/W2002357820","https://openalex.org/W2334216590","https://openalex.org/W2997206142","https://openalex.org/W2027962246","https://openalex.org/W2244442793","https://openalex.org/W2107449083"],"abstract_inverted_index":{"This":[0],"paper":[1],"studies":[2],"a":[3,68],"class":[4],"of":[5,54,106,115,124],"linear":[6,46,126],"regulator":[7,48,127],"problem":[8,23,80],"where":[9],"the":[10,37,44,58,104,112,116,121,125],"terminal":[11,117],"payoff":[12,118],"function":[13,20,123],"is":[14,24,62,76,82],"not":[15,26,32],"necessarily":[16],"quadratic.":[17],"The":[18,51],"value":[19,122],"for":[21,43,78],"this":[22,66,79],"generally":[25],"quadratic":[27,47],"and":[28,88],"thus":[29],"it":[30],"can":[31,100],"be":[33,85,101],"reduced":[34],"to":[35,84,111,119],"solving":[36],"corresponding":[38],"matrix":[39],"Riccati":[40],"equation":[41],"as":[42,103],"standard":[45],"(LQR)":[49],"problem.":[50,128],"computational":[52,70],"method":[53,71],"direct":[55],"iteration":[56],"using":[57],"dynamic":[59],"programming":[60],"equations":[61],"computationally":[63],"expensive.":[64],"In":[65,91],"paper,":[67],"new":[69],"based":[72],"on":[73],"max-plus":[74,94,107,113],"techniques":[75],"developed":[77],"which":[81,99],"demonstrated":[83],"more":[86,89],"efficient":[87],"accurate.":[90],"particular,":[92],"three":[93],"fundamental":[95],"solutions":[96],"are":[97],"obtained":[98],"used":[102],"kernel":[105],"integration":[108],"with":[109],"respect":[110],"dual":[114],"generate":[120]},"counts_by_year":[{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
