{"id":"https://openalex.org/W2116292651","doi":"https://doi.org/10.1109/tac.2010.2103416","title":"Stability Margin Scaling Laws for Distributed Formation Control as a Function of Network Structure","display_name":"Stability Margin Scaling Laws for Distributed Formation Control as a Function of Network Structure","publication_year":2011,"publication_date":"2011-01-07","ids":{"openalex":"https://openalex.org/W2116292651","doi":"https://doi.org/10.1109/tac.2010.2103416","mag":"2116292651"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2010.2103416","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2103416","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1005.0351","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"He Hao","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"He Hao","raw_affiliation_strings":["Department of Mechanical and AeroSpace Engineering, University of Florida, Gainesville, FL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and AeroSpace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Prabir Barooah","orcid":null},"institutions":[{"id":"https://openalex.org/I33213144","display_name":"University of Florida","ror":"https://ror.org/02y3ad647","country_code":"US","type":"education","lineage":["https://openalex.org/I33213144"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Prabir Barooah","raw_affiliation_strings":["Department of Mechanical and AeroSpace Engineering, University of Florida, Gainesville, FL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical and AeroSpace Engineering, University of Florida, Gainesville, FL, USA","institution_ids":["https://openalex.org/I33213144"]}]},{"author_position":"last","author":{"id":null,"display_name":"Prashant G. Mehta","orcid":null},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Prashant G. Mehta","raw_affiliation_strings":["Science Laboratory, Department of Mechanical Science and Engineering, University of Illinois, Urbana-Champaign, Urbana, IL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Science Laboratory, Department of Mechanical Science and Engineering, University of Illinois, Urbana-Champaign, Urbana, IL, USA","institution_ids":["https://openalex.org/I157725225"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.7541,"has_fulltext":false,"cited_by_count":64,"citation_normalized_percentile":{"value":0.95067863,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"56","issue":"4","first_page":"923","last_page":"929"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.692799985408783,"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"}},"topics":[{"id":"https://openalex.org/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.692799985408783,"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"}},{"id":"https://openalex.org/T10524","display_name":"Traffic control and management","score":0.14480000734329224,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.04270000010728836,"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/exponential-stability","display_name":"Exponential stability","score":0.6557000279426575},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.6539000272750854},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5217999815940857},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.49380001425743103},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.47929999232292175},{"id":"https://openalex.org/keywords/exponent","display_name":"Exponent","score":0.44929999113082886},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.4442000091075897},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.43209999799728394},{"id":"https://openalex.org/keywords/margin","display_name":"Margin (machine learning)","score":0.4146000146865845}],"concepts":[{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.6557000279426575},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.6539000272750854},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6039000153541565},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5217999815940857},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.49380001425743103},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.47929999232292175},{"id":"https://openalex.org/C2780388253","wikidata":"https://www.wikidata.org/wiki/Q5421508","display_name":"Exponent","level":2,"score":0.44929999113082886},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.4442000091075897},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43720000982284546},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.43209999799728394},{"id":"https://openalex.org/C774472","wikidata":"https://www.wikidata.org/wiki/Q6760393","display_name":"Margin (machine learning)","level":2,"score":0.4146000146865845},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3659000098705292},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.35929998755455017},{"id":"https://openalex.org/C38976095","wikidata":"https://www.wikidata.org/wiki/Q752641","display_name":"Asymmetry","level":2,"score":0.3449999988079071},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.32429999113082886},{"id":"https://openalex.org/C2988430800","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Scaling law","level":3,"score":0.3131999969482422},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.3050000071525574},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.29499998688697815},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2768999934196472},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.27619999647140503},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27250000834465027},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2721000015735626},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.26980000734329224},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.259799987077713},{"id":"https://openalex.org/C4292930","wikidata":"https://www.wikidata.org/wiki/Q17009341","display_name":"Distributed element model","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C32946077","wikidata":"https://www.wikidata.org/wiki/Q618079","display_name":"Network analysis","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tac.2010.2103416","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2010.2103416","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:1005.0351","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1005.0351","pdf_url":"https://arxiv.org/pdf/1005.0351","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1005.0351","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1005.0351","pdf_url":"https://arxiv.org/pdf/1005.0351","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W2019950225","https://openalex.org/W2049644788","https://openalex.org/W2097992179","https://openalex.org/W2100498500","https://openalex.org/W2107415588","https://openalex.org/W2124451866","https://openalex.org/W2130181194","https://openalex.org/W2146890818","https://openalex.org/W6683714705"],"related_works":[],"abstract_inverted_index":{"We":[0,26,46,113],"describe":[1],"a":[2,12,20,37,77,95,116],"methodology":[3],"for":[4,30,55],"modeling,":[5],"analysis":[6],"and":[7,68],"distributed":[8],"control":[9,71,111],"design":[10],"of":[11,43,64,81,118],"large":[13],"vehicular":[14],"formation":[15],"whose":[16],"information":[17,66,98],"graph":[18,67,99],"is":[19,59],"<i":[21],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[22],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">D</i>":[23],"-dimensional":[24],"lattice.":[25],"derive":[27],"asymptotic":[28],"formulae":[29],"the":[31,44,49,52,56,62,65,70,86,107,119,123],"closed-loop":[32],"stability":[33,57],"margin":[34,58],"based":[35],"on":[36],"partial":[38],"differential":[39],"equation":[40],"(PDE)":[41],"approximation":[42],"formation.":[45],"show":[47,84],"that":[48,85],"exponent":[50],"in":[51,106],"scaling":[53,87],"law":[54,88],"influenced":[60],"by":[61,69,93,101,122],"structure":[63],"architecture":[72],"(symmetric":[73],"or":[74],"asymmetric).":[75],"For":[76],"given":[78],"fixed":[79],"number":[80],"vehicles,":[82],"we":[83],"can":[89],"be":[90],"improved":[91],"significantly":[92],"employing":[94],"higher":[96],"dimensional":[97],"and/or":[100],"introducing":[102],"small":[103],"asymmetry":[104],"(mistuning)":[105],"nominally":[108],"symmetric":[109],"proportional":[110],"gains.":[112],"also":[114],"provide":[115],"characterization":[117],"error":[120],"introduced":[121],"PDE":[124],"approximation.":[125]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":5},{"year":2012,"cited_by_count":6}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}