{"id":"https://openalex.org/W3096684992","doi":"https://doi.org/10.1109/tac.2020.3034206","title":"Discrete-Time Differential Dynamic Programming on Lie Groups: Derivation, Convergence Analysis, and Numerical Results","display_name":"Discrete-Time Differential Dynamic Programming on Lie Groups: Derivation, Convergence Analysis, and Numerical Results","publication_year":2020,"publication_date":"2020-10-29","ids":{"openalex":"https://openalex.org/W3096684992","doi":"https://doi.org/10.1109/tac.2020.3034206","mag":"3096684992"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2020.3034206","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.3034206","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/A5043052033","display_name":"George I. Boutselis","orcid":"https://orcid.org/0000-0002-0930-3257"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]},{"id":"https://openalex.org/I1332737386","display_name":"General Electric (United States)","ror":"https://ror.org/013msgt25","country_code":"US","type":"company","lineage":["https://openalex.org/I1332737386"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"George I. Boutselis","raw_affiliation_strings":["Aerospace Engineering Department, Georgia Institute of Technology, Atlanta, GA, USA","Controls and Optimization Group, General Electric Research, Niskayuna, NY, USA"],"raw_orcid":"https://orcid.org/0000-0002-0930-3257","affiliations":[{"raw_affiliation_string":"Aerospace Engineering Department, Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Controls and Optimization Group, General Electric Research, Niskayuna, NY, USA","institution_ids":["https://openalex.org/I1332737386"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044505993","display_name":"Evangelos A. Theodorou","orcid":"https://orcid.org/0000-0002-0834-5738"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Evangelos Theodorou","raw_affiliation_strings":["Aerospace Engineering Department, Georgia Institute of Technology, Atlanta, GA, USA"],"raw_orcid":"https://orcid.org/0000-0002-0834-5738","affiliations":[{"raw_affiliation_string":"Aerospace Engineering Department, Georgia Institute of Technology, Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0801,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.87039595,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"66","issue":"10","first_page":"4636","last_page":"4651"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9984999895095825,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9984999895095825,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9980999827384949,"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":0.9966999888420105,"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/differential-dynamic-programming","display_name":"Differential dynamic programming","score":0.8211129307746887},{"id":"https://openalex.org/keywords/lie-group","display_name":"Lie group","score":0.6752656102180481},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6633821129798889},{"id":"https://openalex.org/keywords/dynamic-programming","display_name":"Dynamic programming","score":0.6520700454711914},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.5481141805648804},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.5382653474807739},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5162068009376526},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5118078589439392},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46080446243286133},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.45098575949668884},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.4406258165836334},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4131668210029602},{"id":"https://openalex.org/keywords/lie-algebra","display_name":"Lie algebra","score":0.4131064713001251},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.41222280263900757},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3724742531776428},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3531373143196106},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.21903589367866516}],"concepts":[{"id":"https://openalex.org/C92292787","wikidata":"https://www.wikidata.org/wiki/Q5275342","display_name":"Differential dynamic programming","level":3,"score":0.8211129307746887},{"id":"https://openalex.org/C187915474","wikidata":"https://www.wikidata.org/wiki/Q622679","display_name":"Lie group","level":2,"score":0.6752656102180481},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6633821129798889},{"id":"https://openalex.org/C37404715","wikidata":"https://www.wikidata.org/wiki/Q380679","display_name":"Dynamic programming","level":2,"score":0.6520700454711914},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.5481141805648804},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.5382653474807739},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5162068009376526},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5118078589439392},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46080446243286133},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.45098575949668884},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.4406258165836334},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4131668210029602},{"id":"https://openalex.org/C51568863","wikidata":"https://www.wikidata.org/wiki/Q664495","display_name":"Lie algebra","level":2,"score":0.4131064713001251},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.41222280263900757},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3724742531776428},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3531373143196106},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.21903589367866516},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2020.3034206","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2020.3034206","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":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":48,"referenced_works":["https://openalex.org/W331199924","https://openalex.org/W658381347","https://openalex.org/W1510199534","https://openalex.org/W1528604627","https://openalex.org/W1538183267","https://openalex.org/W1540059687","https://openalex.org/W1544770838","https://openalex.org/W1566164999","https://openalex.org/W1622730090","https://openalex.org/W1632150706","https://openalex.org/W1681287014","https://openalex.org/W1804110266","https://openalex.org/W1841697596","https://openalex.org/W1964946446","https://openalex.org/W2002948623","https://openalex.org/W2025752438","https://openalex.org/W2049105993","https://openalex.org/W2049424664","https://openalex.org/W2061356302","https://openalex.org/W2068657282","https://openalex.org/W2071355416","https://openalex.org/W2098432798","https://openalex.org/W2101341777","https://openalex.org/W2108631580","https://openalex.org/W2109944946","https://openalex.org/W2119135605","https://openalex.org/W2126147262","https://openalex.org/W2128285126","https://openalex.org/W2164259133","https://openalex.org/W2170039048","https://openalex.org/W2288947144","https://openalex.org/W2329300820","https://openalex.org/W2342744866","https://openalex.org/W2495681058","https://openalex.org/W2497511204","https://openalex.org/W2793020180","https://openalex.org/W2954172414","https://openalex.org/W4205293427","https://openalex.org/W4248185632","https://openalex.org/W4285719527","https://openalex.org/W4292402580","https://openalex.org/W4301014524","https://openalex.org/W4388322878","https://openalex.org/W6632380756","https://openalex.org/W6638753824","https://openalex.org/W6668322159","https://openalex.org/W6674995601","https://openalex.org/W6676444349"],"related_works":["https://openalex.org/W4281717838","https://openalex.org/W2212478920","https://openalex.org/W4315488747","https://openalex.org/W2007971149","https://openalex.org/W761054003","https://openalex.org/W3012421647","https://openalex.org/W2052479296","https://openalex.org/W2602009922","https://openalex.org/W2166339378","https://openalex.org/W1996983632"],"abstract_inverted_index":{"We":[0],"develop":[1],"a":[2,24,65,94],"discrete-time":[3],"optimal":[4],"control":[5,61],"framework":[6],"for":[7,28,43],"systems":[8],"evolving":[9],"on":[10,49,97],"Lie":[11,50],"groups.":[12,51],"Our":[13],"article":[14],"generalizes":[15],"the":[16,37,60,69,75,84],"original":[17],"differential":[18],"dynamic":[19],"programming":[20],"method,":[21],"by":[22],"employing":[23],"coordinate-free,":[25],"Lie-theoretic":[26],"approach":[27],"its":[29],"derivation.":[30],"A":[31],"key":[32],"element":[33],"lies,":[34],"specifically,":[35],"in":[36],"use":[38],"of":[39,59,88],"quadratic":[40],"expansion":[41],"schemes":[42],"cost":[44],"functions":[45],"and":[46,86],"dynamics":[47],"defined":[48],"The":[52],"obtained":[53],"algorithm":[54],"iteratively":[55],"optimizes":[56],"local":[57],"approximations":[58],"problem,":[62],"until":[63],"reaching":[64],"(sub)optimal":[66],"solution.":[67],"On":[68],"theoretical":[70],"side,":[71],"we":[72],"also":[73],"study":[74],"conditions":[76],"under":[77],"which":[78],"convergence":[79],"is":[80],"attained.":[81],"Details":[82],"about":[83],"behavior":[85],"implementation":[87],"our":[89],"method":[90],"are":[91],"provided":[92],"through":[93],"simulated":[95],"example":[96],"<inline-formula":[98],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[99],"xmlns:xlink=\"http://www.w3.org/1999/xlink\"><tex-math":[100],"notation=\"LaTeX\">$TSO(3)$</tex-math></inline-formula>":[101],".":[102]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
