{"id":"https://openalex.org/W1794529597","doi":"https://doi.org/10.1109/tac.2017.2668380","title":"Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design","display_name":"Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design","publication_year":2017,"publication_date":"2017-02-13","ids":{"openalex":"https://openalex.org/W1794529597","doi":"https://doi.org/10.1109/tac.2017.2668380","mag":"1794529597"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2017.2668380","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2668380","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1503.03144","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026600708","display_name":"Ian R. Manchester","orcid":"https://orcid.org/0000-0002-7035-3173"},"institutions":[{"id":"https://openalex.org/I129604602","display_name":"University of Sydney","ror":"https://ror.org/0384j8v12","country_code":"AU","type":"education","lineage":["https://openalex.org/I129604602"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Ian R. Manchester","raw_affiliation_strings":["[Australian Centre for Field Robotics and the School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney, NSW, Australia]"],"affiliations":[{"raw_affiliation_string":"[Australian Centre for Field Robotics and the School of Aerospace, Mechanical and Mechatronic Engineering, University of Sydney, Sydney, NSW, Australia]","institution_ids":["https://openalex.org/I129604602"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044026747","display_name":"Jean-Jacques Slotine","orcid":"https://orcid.org/0000-0002-7161-7812"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jean-Jacques E. Slotine","raw_affiliation_strings":["[Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, MA, USA]"],"affiliations":[{"raw_affiliation_string":"[Nonlinear Systems Laboratory, Massachusetts Institute of Technology, Cambridge, MA, USA]","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026600708"],"corresponding_institution_ids":["https://openalex.org/I129604602"],"apc_list":null,"apc_paid":null,"fwci":0.8154,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.72718275,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"62","issue":"6","first_page":"3046","last_page":"3053"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10791","display_name":"Advanced Control Systems Optimization","score":0.9789000153541565,"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":0.9779000282287598,"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/convexity","display_name":"Convexity","score":0.7486745119094849},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6666025519371033},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6481349468231201},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.6410596966743469},{"id":"https://openalex.org/keywords/submanifold","display_name":"Submanifold","score":0.602724015712738},{"id":"https://openalex.org/keywords/constructive","display_name":"Constructive","score":0.5730184316635132},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.5354174971580505},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4892251491546631},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.485823392868042},{"id":"https://openalex.org/keywords/nonlinear-control","display_name":"Nonlinear control","score":0.4723305106163025},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4415152072906494},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3797091841697693},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36867380142211914},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2521793246269226},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2307385802268982},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1819845736026764}],"concepts":[{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7486745119094849},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6666025519371033},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6481349468231201},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.6410596966743469},{"id":"https://openalex.org/C151300846","wikidata":"https://www.wikidata.org/wiki/Q125539","display_name":"Submanifold","level":2,"score":0.602724015712738},{"id":"https://openalex.org/C2778701210","wikidata":"https://www.wikidata.org/wiki/Q28130034","display_name":"Constructive","level":3,"score":0.5730184316635132},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.5354174971580505},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4892251491546631},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.485823392868042},{"id":"https://openalex.org/C91581856","wikidata":"https://www.wikidata.org/wiki/Q2707001","display_name":"Nonlinear control","level":3,"score":0.4723305106163025},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4415152072906494},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3797091841697693},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36867380142211914},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2521793246269226},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2307385802268982},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1819845736026764},{"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/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1109/tac.2017.2668380","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2017.2668380","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"},{"id":"pmh:oai:arXiv.org:1503.03144","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.03144","pdf_url":"https://arxiv.org/pdf/1503.03144","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.1503.03144","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1503.03144","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"},{"id":"mag:1794529597","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1503.03144","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1503.03144","pdf_url":"https://arxiv.org/pdf/1503.03144","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6258507168","display_name":null,"funder_award_id":"DP150100577","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"}],"funders":[{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1794529597.pdf","grobid_xml":"https://content.openalex.org/works/W1794529597.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W634426574","https://openalex.org/W1487127700","https://openalex.org/W1537653646","https://openalex.org/W1541665771","https://openalex.org/W1548148540","https://openalex.org/W1566710847","https://openalex.org/W1967184028","https://openalex.org/W1980330256","https://openalex.org/W1996204208","https://openalex.org/W2000714860","https://openalex.org/W2009127079","https://openalex.org/W2015084265","https://openalex.org/W2023126268","https://openalex.org/W2025977958","https://openalex.org/W2026892575","https://openalex.org/W2036216368","https://openalex.org/W2038730444","https://openalex.org/W2041076275","https://openalex.org/W2045938917","https://openalex.org/W2069427876","https://openalex.org/W2070412653","https://openalex.org/W2077205953","https://openalex.org/W2083483041","https://openalex.org/W2090167557","https://openalex.org/W2096947533","https://openalex.org/W2101170197","https://openalex.org/W2103624276","https://openalex.org/W2104730516","https://openalex.org/W2105365768","https://openalex.org/W2105758800","https://openalex.org/W2110360108","https://openalex.org/W2117079884","https://openalex.org/W2118646441","https://openalex.org/W2128928412","https://openalex.org/W2132238259","https://openalex.org/W2133404041","https://openalex.org/W2134889984","https://openalex.org/W2135234927","https://openalex.org/W2137002893","https://openalex.org/W2138025249","https://openalex.org/W2140515911","https://openalex.org/W2140531311","https://openalex.org/W2152112251","https://openalex.org/W2161367843","https://openalex.org/W2165861322","https://openalex.org/W2273683766","https://openalex.org/W2312915715","https://openalex.org/W2320012146","https://openalex.org/W2322760626","https://openalex.org/W2492791808","https://openalex.org/W2536620281","https://openalex.org/W2734465626","https://openalex.org/W2735665324","https://openalex.org/W2736611203","https://openalex.org/W2749408143","https://openalex.org/W2962786526","https://openalex.org/W3160954918","https://openalex.org/W3210839039","https://openalex.org/W4206033904","https://openalex.org/W4292872153","https://openalex.org/W6741498363"],"related_works":["https://openalex.org/W2047525247","https://openalex.org/W3203905183","https://openalex.org/W3202366558","https://openalex.org/W2029926860","https://openalex.org/W2981969580","https://openalex.org/W2147439098","https://openalex.org/W2951867858","https://openalex.org/W2156102486","https://openalex.org/W2053499273","https://openalex.org/W2963924910","https://openalex.org/W1552488793","https://openalex.org/W1832874869","https://openalex.org/W2032190018","https://openalex.org/W2155689575","https://openalex.org/W3170533802","https://openalex.org/W71948162","https://openalex.org/W1481077264","https://openalex.org/W3115581221","https://openalex.org/W2117670637","https://openalex.org/W2021374641"],"abstract_inverted_index":{"We":[0,17,53,82],"introduce":[1],"the":[2,84],"concept":[3],"of":[4,24,27,75,79,86],"a":[5,28,35,43,76,90,105],"control":[6,15,30],"contraction":[7,10],"metric,":[8],"extending":[9],"analysis":[11],"to":[12],"constructive":[13],"nonlinear":[14,29,77],"design.":[16],"derive":[18,68],"sufficient":[19,61],"conditions":[20,33,57],"for":[21,62,72,92],"exponential":[22,73],"stabilizability":[23],"all":[25],"trajectories":[26],"system.":[31],"The":[32],"have":[34],"simple":[36],"geometrical":[37],"interpretation,":[38],"can":[39],"be":[40],"written":[41],"as":[42],"convex":[44,70],"feasibility":[45],"problem,":[46],"and":[47,60,66,101],"are":[48,58],"invariant":[49],"under":[50],"coordinate":[51],"changes.":[52],"show":[54],"that":[55,97],"these":[56],"necessary":[59],"feedback":[63],"linearizable":[64],"systems,":[65],"also":[67],"novel":[69],"criteria":[71],"stabilization":[74],"submanifold":[78],"state":[80],"space.":[81],"illustrate":[83],"benefits":[85],"convexity":[87],"by":[88],"constructing":[89],"controller":[91],"an":[93],"unstable":[94],"polynomial":[95],"system":[96],"combines":[98],"local":[99],"optimality":[100],"global":[102],"stability,":[103],"using":[104],"metric":[106],"found":[107],"via":[108],"sum-of-squares":[109],"programming.":[110]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
