{"id":"https://openalex.org/W2004213221","doi":"https://doi.org/10.1109/cdc.2007.4434051","title":"Approximate solutions of the regulator equations for nonlinear DPS","display_name":"Approximate solutions of the regulator equations for nonlinear DPS","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2004213221","doi":"https://doi.org/10.1109/cdc.2007.4434051","mag":"2004213221"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2007.4434051","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434051","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th 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/A5110332655","display_name":"C.I. Byrnes","orcid":null},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]},{"id":"https://openalex.org/I204465549","display_name":"Washington University in St. Louis","ror":"https://ror.org/01yc7t268","country_code":"US","type":"education","lineage":["https://openalex.org/I204465549"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"C.I. Byrnes","raw_affiliation_strings":["Washington University, Saint Louis, MO, USA","Washington Univ., Washington"],"affiliations":[{"raw_affiliation_string":"Washington University, Saint Louis, MO, USA","institution_ids":["https://openalex.org/I204465549"]},{"raw_affiliation_string":"Washington Univ., Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085969777","display_name":"D.S. Gilliam","orcid":"https://orcid.org/0000-0002-5416-6191"},"institutions":[{"id":"https://openalex.org/I12315562","display_name":"Texas Tech University","ror":"https://ror.org/0405mnx93","country_code":"US","type":"education","lineage":["https://openalex.org/I12315562"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D.S. Gilliam","raw_affiliation_strings":["Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA","Mathematics and Statistics at Texas Tech University, Lubbock, USA"],"affiliations":[{"raw_affiliation_string":"Mathematics and Statistics, Texas Tech University, Lubbock, TX, USA","institution_ids":["https://openalex.org/I12315562"]},{"raw_affiliation_string":"Mathematics and Statistics at Texas Tech University, Lubbock, USA","institution_ids":["https://openalex.org/I12315562"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5110332655"],"corresponding_institution_ids":["https://openalex.org/I201448701","https://openalex.org/I204465549"],"apc_list":null,"apc_paid":null,"fwci":0.8709,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.7948553,"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":"854","last_page":"859"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","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/T11110","display_name":"Stability and Controllability of Differential Equations","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/T11416","display_name":"Numerical methods for differential equations","score":0.9943000078201294,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9937000274658203,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/regulator","display_name":"Regulator","score":0.7824927568435669},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7598398923873901},{"id":"https://openalex.org/keywords/linear-quadratic-regulator","display_name":"Linear-quadratic regulator","score":0.677299976348877},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5766578912734985},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5644314289093018},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.4566878080368042},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4399992525577545},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.43761271238327026},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.431610643863678},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32370513677597046},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29132080078125},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.2194623053073883},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09147074818611145},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.057303786277770996}],"concepts":[{"id":"https://openalex.org/C6929976","wikidata":"https://www.wikidata.org/wiki/Q3771881","display_name":"Regulator","level":3,"score":0.7824927568435669},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7598398923873901},{"id":"https://openalex.org/C98779006","wikidata":"https://www.wikidata.org/wiki/Q2520550","display_name":"Linear-quadratic regulator","level":3,"score":0.677299976348877},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5766578912734985},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5644314289093018},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.4566878080368042},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4399992525577545},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.43761271238327026},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.431610643863678},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32370513677597046},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29132080078125},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.2194623053073883},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09147074818611145},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.057303786277770996},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2007.4434051","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2007.4434051","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2007 46th IEEE Conference on Decision and Control","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":18,"referenced_works":["https://openalex.org/W610804881","https://openalex.org/W1487112583","https://openalex.org/W1491218311","https://openalex.org/W1543420164","https://openalex.org/W1559539328","https://openalex.org/W2011735434","https://openalex.org/W2048043446","https://openalex.org/W2054365094","https://openalex.org/W2069477977","https://openalex.org/W2086906338","https://openalex.org/W2119925384","https://openalex.org/W2149862906","https://openalex.org/W2163245660","https://openalex.org/W2312915715","https://openalex.org/W2502990994","https://openalex.org/W4205940976","https://openalex.org/W4213367573","https://openalex.org/W4249919931"],"related_works":["https://openalex.org/W2731754693","https://openalex.org/W267916353","https://openalex.org/W3091102817","https://openalex.org/W2326995340","https://openalex.org/W1985169903","https://openalex.org/W2152693275","https://openalex.org/W311622956","https://openalex.org/W1592622096","https://openalex.org/W4283732277","https://openalex.org/W2122083069"],"abstract_inverted_index":{"One":[0],"of":[1,9,20,46,57,99,112],"our":[2],"overall":[3],"research":[4],"goals":[5],"is":[6,93],"the":[7,34,58,82,87,110],"design":[8],"feedback":[10],"control":[11],"laws":[12],"that":[13],"can":[14],"be":[15],"used":[16],"to":[17,95],"solve":[18],"problems":[19],"output":[21],"regulation":[22],"for":[23,53,61],"nonlinear":[24,40,62],"distributed":[25],"parameter":[26],"systems":[27],"(DPS).":[28],"Towards":[29],"this":[30],"end,":[31],"we":[32,48],"recast":[33],"well-known":[35],"regulator":[36,59,83],"equations":[37,84],"as":[38],"a":[39,50,96,100,105],"fixed":[41,71],"point":[42,72],"problem":[43,60],"in":[44],"terms":[45],"which":[47],"derive":[49],"numerical":[51,65,114],"algorithm":[52],"obtaining":[54],"approximate":[55],"solutions":[56],"DPS.":[63],"The":[64,91],"methods":[66],"are":[67],"based":[68],"on":[69],"either":[70],"or":[73],"Newton":[74],"iteration":[75],"with":[76,86,104],"initial":[77],"state":[78],"obtained":[79],"by":[80],"solving":[81],"associated":[85],"corresponding":[88],"linearized":[89],"problem.":[90],"method":[92],"applied":[94],"specific":[97],"example":[98],"reaction":[101],"diffusion":[102],"equation":[103],"quadratic":[106],"nonlinearity.":[107],"We":[108],"present":[109],"results":[111],"two":[113],"simulations.":[115]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}