{"id":"https://openalex.org/W2140452807","doi":"https://doi.org/10.1137/s0363012903425568","title":"Characterization of Gradient Control Systems","display_name":"Characterization of Gradient Control Systems","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2140452807","doi":"https://doi.org/10.1137/s0363012903425568","mag":"2140452807"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012903425568","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012903425568","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research.rug.nl/en/publications/196fc260-3adf-43a3-88d2-f32ed94600cb","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027913099","display_name":"Jorge Cort\u00e9s","orcid":"https://orcid.org/0000-0001-9582-5184"},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jorge Cort\u00e9s","raw_affiliation_strings":["Department of Applied Mathematics and Statistics, University of California at Santa Cruz, 1156 High Street, Santa Cruz, CA 95064"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Statistics, University of California at Santa Cruz, 1156 High Street, Santa Cruz, CA 95064","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005018540","display_name":"Arjan van der Schaft","orcid":"https://orcid.org/0000-0002-2383-9234"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arjan van der Schaft","raw_affiliation_strings":["Systems, Control and Applied Analysis"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Systems, Control and Applied Analysis","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042898289","display_name":"P.E. Crouch","orcid":null},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter E. Crouch","raw_affiliation_strings":["Department of Electrical and Computer Engineering, Arizona State University, Tempe, AZ 85287"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Computer Engineering, Arizona State University, Tempe, AZ 85287","institution_ids":["https://openalex.org/I55732556"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3661,"has_fulltext":true,"cited_by_count":55,"citation_normalized_percentile":{"value":0.92904136,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"4","first_page":"1192","last_page":"1214"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9787999987602234,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9787999987602234,"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/T12763","display_name":"ATP Synthase and ATPases Research","score":0.9757999777793884,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9735999703407288,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/affine-connection","display_name":"Affine connection","score":0.8716868758201599},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7963651418685913},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6881957054138184},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.6064333319664001},{"id":"https://openalex.org/keywords/levi-civita-connection","display_name":"Levi-Civita connection","score":0.5227139592170715},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42932796478271484},{"id":"https://openalex.org/keywords/affine-hull","display_name":"Affine hull","score":0.4247817397117615},{"id":"https://openalex.org/keywords/metric-space","display_name":"Metric space","score":0.41005682945251465},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33953243494033813},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.33473533391952515},{"id":"https://openalex.org/keywords/fundamental-theorem-of-riemannian-geometry","display_name":"Fundamental theorem of Riemannian geometry","score":0.33083170652389526},{"id":"https://openalex.org/keywords/affine-space","display_name":"Affine space","score":0.28262466192245483},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.23168671131134033},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17526182532310486},{"id":"https://openalex.org/keywords/ricci-curvature","display_name":"Ricci curvature","score":0.14503055810928345},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1408071219921112},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06150251626968384}],"concepts":[{"id":"https://openalex.org/C105561566","wikidata":"https://www.wikidata.org/wiki/Q1371213","display_name":"Affine connection","level":3,"score":0.8716868758201599},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7963651418685913},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6881957054138184},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.6064333319664001},{"id":"https://openalex.org/C129049296","wikidata":"https://www.wikidata.org/wiki/Q548675","display_name":"Levi-Civita connection","level":5,"score":0.5227139592170715},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42932796478271484},{"id":"https://openalex.org/C112128483","wikidata":"https://www.wikidata.org/wiki/Q382504","display_name":"Affine hull","level":4,"score":0.4247817397117615},{"id":"https://openalex.org/C198043062","wikidata":"https://www.wikidata.org/wiki/Q180953","display_name":"Metric space","level":2,"score":0.41005682945251465},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33953243494033813},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.33473533391952515},{"id":"https://openalex.org/C4306028","wikidata":"https://www.wikidata.org/wiki/Q2185349","display_name":"Fundamental theorem of Riemannian geometry","level":4,"score":0.33083170652389526},{"id":"https://openalex.org/C173110770","wikidata":"https://www.wikidata.org/wiki/Q382698","display_name":"Affine space","level":3,"score":0.28262466192245483},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.23168671131134033},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17526182532310486},{"id":"https://openalex.org/C12089564","wikidata":"https://www.wikidata.org/wiki/Q1195879","display_name":"Ricci curvature","level":3,"score":0.14503055810928345},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1408071219921112},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06150251626968384},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/s0363012903425568","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012903425568","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:pure.rug.nl:openaire/196fc260-3adf-43a3-88d2-f32ed94600cb","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/196fc260-3adf-43a3-88d2-f32ed94600cb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cort\u00e9s, J, Schaft, A V D & Crouch, P E 2005, 'Characterization of Gradient Control Systems', SIAM Journal on Control and Optimization, vol. 44, no. 4, pp. 1192 - 1214.","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:ris.utwente.nl:openaire/9dadcbcc-f2af-4fb9-884c-3cb709d3be43","is_oa":true,"landing_page_url":"https://research.utwente.nl/en/publications/9dadcbcc-f2af-4fb9-884c-3cb709d3be43","pdf_url":null,"source":{"id":"https://openalex.org/S4406922991","display_name":"University of Twente Research Information","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cort\u00e9s, J, van der Schaft, A & Crouch, P E 2005, 'Characterization of gradient control systems', SIAM journal on control and optimization, vol. 44, no. 4, pp. 1192-1214. https://doi.org/10.1137/S0363012903425568","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.14.745","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.14.745","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://motion.csl.uiuc.edu/~jorge/papers/CoScCr03.pdf.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.234.6309","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.234.6309","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/math/0303371v1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.391.3095","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.391.3095","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://tintoretto.ucsd.edu/jorge/publications/data/2003_CoScCr-sicon.pdf","raw_type":"text"},{"id":"pmh:oai:pure.rug.nl:openaire_cris_publications/196fc260-3adf-43a3-88d2-f32ed94600cb","is_oa":true,"landing_page_url":"https://hdl.handle.net/11370/196fc260-3adf-43a3-88d2-f32ed94600cb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Cort\u00e9s, J, Schaft, A V D & Crouch, P E 2005, 'Characterization of Gradient Control Systems', SIAM Journal on Control and Optimization, vol. 44, no. 4, pp. 1192 - 1214.","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:pure.rug.nl:openaire/196fc260-3adf-43a3-88d2-f32ed94600cb","is_oa":true,"landing_page_url":"https://research.rug.nl/en/publications/196fc260-3adf-43a3-88d2-f32ed94600cb","pdf_url":null,"source":{"id":"https://openalex.org/S4306400420","display_name":"University of Groningen research database (University of Groningen / Centre for Information Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I169381384","host_organization_name":"University of Groningen","host_organization_lineage":["https://openalex.org/I169381384"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Cort\u00e9s, J, Schaft, A V D & Crouch, P E 2005, 'Characterization of Gradient Control Systems', SIAM Journal on Control and Optimization, vol. 44, no. 4, pp. 1192 - 1214.","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5122138610","display_name":"Perturbation Methods for Nonlinear Control of Lagrangian Systems","funder_award_id":"0100162","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W57077127","https://openalex.org/W582187134","https://openalex.org/W1540014537","https://openalex.org/W1563705581","https://openalex.org/W1959414294","https://openalex.org/W1970464464","https://openalex.org/W2009310522","https://openalex.org/W2047108956","https://openalex.org/W2048889103","https://openalex.org/W2058113136","https://openalex.org/W2068002984","https://openalex.org/W2076467525","https://openalex.org/W2092907184","https://openalex.org/W2108093366","https://openalex.org/W2135404129","https://openalex.org/W2140998418","https://openalex.org/W2146826877","https://openalex.org/W2172002220","https://openalex.org/W2497483184","https://openalex.org/W2562183967","https://openalex.org/W2562786109","https://openalex.org/W3038420293","https://openalex.org/W4206033904","https://openalex.org/W4206651632","https://openalex.org/W4213284467","https://openalex.org/W4230093189","https://openalex.org/W4292402580"],"related_works":["https://openalex.org/W2489785590","https://openalex.org/W3118825917","https://openalex.org/W2963793293","https://openalex.org/W2613657242","https://openalex.org/W2337424520","https://openalex.org/W4301836370","https://openalex.org/W1524907630","https://openalex.org/W2326744899","https://openalex.org/W4388931862","https://openalex.org/W2555295794"],"abstract_inverted_index":{"Given":[0],"a":[1,10,40,63,100],"general":[2],"nonlinear":[3],"affine":[4,12,57,76,97],"control":[5,34,42],"system":[6,35,43,70,86],"with":[7,71,95],"outputs":[8],"and":[9,28,78,87],"torsion-free":[11],"connection":[13,51,98],"defined":[14],"on":[15,62,79],"its":[16],"state":[17],"space,":[18],"we":[19,25],"investigate":[20],"the":[21,33,55,69,74,80,84,88,104],"gradient":[22,41,89],"realization":[23],"problem:":[24],"give":[26],"necessary":[27],"sufficient":[29],"conditions":[30],"under":[31],"which":[32],"can":[36],"be":[37],"written":[38],"as":[39],"corresponding":[44],"to":[45,54,73],"some":[46],"pseudo-Riemannian":[47],"metric":[48],"whose":[49],"Levi-Civita":[50],"is":[52],"equal":[53],"given":[56,75],"connection.":[58],"The":[59,91],"results":[60],"rely":[61],"suitable":[64],"notion":[65],"of":[66,68,83],"compatibility":[67],"respect":[72],"connection,":[77],"output":[81],"behavior":[82],"prolonged":[85],"extension.":[90],"symmetric":[92],"product":[93],"associated":[94],"an":[96],"plays":[99],"key":[101],"role":[102],"throughout":[103],"discussion.":[105]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
