{"id":"https://openalex.org/W2130393416","doi":"https://doi.org/10.1109/cdc.2010.5717354","title":"An adjoint method for second-order switching time optimization","display_name":"An adjoint method for second-order switching time optimization","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W2130393416","doi":"https://doi.org/10.1109/cdc.2010.5717354","mag":"2130393416"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2010.5717354","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717354","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE 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/A5111628533","display_name":"Timothy M. Caldwell","orcid":null},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"T. M. Caldwell","raw_affiliation_strings":["Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Il. 60208 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Il. 60208 USA","institution_ids":["https://openalex.org/I111979921"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067725461","display_name":"Todd D. Murphey","orcid":"https://orcid.org/0000-0003-2262-8176"},"institutions":[{"id":"https://openalex.org/I111979921","display_name":"Northwestern University","ror":"https://ror.org/000e0be47","country_code":"US","type":"education","lineage":["https://openalex.org/I111979921"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"T. D. Murphey","raw_affiliation_strings":["Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Il. 60208 USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, Evanston, IL, USA","institution_ids":["https://openalex.org/I111979921"]},{"raw_affiliation_string":"Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, Il. 60208 USA","institution_ids":["https://openalex.org/I111979921"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111628533"],"corresponding_institution_ids":["https://openalex.org/I111979921"],"apc_list":null,"apc_paid":null,"fwci":5.7808,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.95811879,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":null,"issue":null,"first_page":"2155","last_page":"2162"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T14083","display_name":"Extremum Seeking Control Systems","score":0.998199999332428,"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/T14083","display_name":"Extremum Seeking Control Systems","score":0.998199999332428,"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":0.9980999827384949,"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":0.9945999979972839,"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/convergence","display_name":"Convergence (economics)","score":0.744902491569519},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.7205756902694702},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5998306274414062},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5536346435546875},{"id":"https://openalex.org/keywords/mode","display_name":"Mode (computer interface)","score":0.5213614702224731},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5028695464134216},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.49747684597969055},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.49533167481422424},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4930994212627411},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.4902265667915344},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.47791939973831177},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4672906994819641},{"id":"https://openalex.org/keywords/first-order","display_name":"First order","score":0.4490514397621155},{"id":"https://openalex.org/keywords/switching-time","display_name":"Switching time","score":0.43421339988708496},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3684878349304199},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3056854009628296},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.14767760038375854}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.744902491569519},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.7205756902694702},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5998306274414062},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5536346435546875},{"id":"https://openalex.org/C48677424","wikidata":"https://www.wikidata.org/wiki/Q6888088","display_name":"Mode (computer interface)","level":2,"score":0.5213614702224731},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5028695464134216},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.49747684597969055},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.49533167481422424},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4930994212627411},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.4902265667915344},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.47791939973831177},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4672906994819641},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.4490514397621155},{"id":"https://openalex.org/C199310435","wikidata":"https://www.wikidata.org/wiki/Q7659121","display_name":"Switching time","level":2,"score":0.43421339988708496},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3684878349304199},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3056854009628296},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.14767760038375854},{"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc.2010.5717354","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2010.5717354","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"49th IEEE Conference on Decision and Control (CDC)","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":24,"referenced_works":["https://openalex.org/W40623226","https://openalex.org/W83533993","https://openalex.org/W227721935","https://openalex.org/W1534096605","https://openalex.org/W1550397500","https://openalex.org/W1570351331","https://openalex.org/W1969811075","https://openalex.org/W2006687959","https://openalex.org/W2098316962","https://openalex.org/W2123224804","https://openalex.org/W2123357397","https://openalex.org/W2125677216","https://openalex.org/W2130519480","https://openalex.org/W2138455707","https://openalex.org/W2152185829","https://openalex.org/W2171717362","https://openalex.org/W2266946488","https://openalex.org/W2580274902","https://openalex.org/W3216584063","https://openalex.org/W6601652627","https://openalex.org/W6632138476","https://openalex.org/W6632994751","https://openalex.org/W6732929567","https://openalex.org/W6804482302"],"related_works":["https://openalex.org/W4292026839","https://openalex.org/W2066101783","https://openalex.org/W2913519323","https://openalex.org/W1966034175","https://openalex.org/W1596524038","https://openalex.org/W3123169305","https://openalex.org/W2132623195","https://openalex.org/W2038392758","https://openalex.org/W2000297171","https://openalex.org/W2734605676"],"abstract_inverted_index":{"Switched":[0],"systems":[1],"evolve":[2],"over":[3],"a":[4,15,19,27],"sequence":[5,21],"of":[6,9,26,35,47,64],"continuous":[7],"modes":[8,13,40],"operation,":[10],"transitioning":[11],"between":[12],"in":[14],"discrete":[16],"manner.":[17],"Assuming":[18],"mode":[20],"is":[22,30],"known,":[23],"the":[24,33,39,62,65],"evolution":[25],"switched":[28],"system":[29],"dictated":[31],"by":[32],"set":[34],"times":[36,50],"for":[37,76],"which":[38],"transition.":[41],"This":[42],"paper":[43],"presents":[44],"second-order":[45,66],"optimization":[46],"these":[48],"switching":[49,57],"and":[51,73],"compares":[52],"its":[53],"convergence":[54,72],"with":[55,89],"first-order":[56,80],"time":[58,86],"optimization.":[59],"We":[60],"emphasize":[61],"importance":[63],"method":[67],"because":[68,74],"it":[69],"exhibits":[70],"quadratic":[71],"even":[75],"relatively":[77],"simple":[78],"examples,":[79],"methods":[81],"fail":[82],"to":[83],"converge":[84],"on":[85],"scales":[87],"compatible":[88],"real-time":[90],"operation.":[91]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":6}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
