{"id":"https://openalex.org/W3086076838","doi":"https://doi.org/10.1109/tcsi.2020.3020146","title":"Adaptive PI Control for Synchronization of Complex Networks With Stochastic Coupling and Nonlinear Dynamics","display_name":"Adaptive PI Control for Synchronization of Complex Networks With Stochastic Coupling and Nonlinear Dynamics","publication_year":2020,"publication_date":"2020-09-11","ids":{"openalex":"https://openalex.org/W3086076838","doi":"https://doi.org/10.1109/tcsi.2020.3020146","mag":"3086076838"},"language":"en","primary_location":{"id":"doi:10.1109/tcsi.2020.3020146","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2020.3020146","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-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/A5004170577","display_name":"Haibo Gu","orcid":"https://orcid.org/0000-0002-1972-4194"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Haibo Gu","raw_affiliation_strings":["Beijing Advanced Innovation Center for Big Data and Brain Computing, School of Automation Science and Electrical Engineering, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-1972-4194","affiliations":[{"raw_affiliation_string":"Beijing Advanced Innovation Center for Big Data and Brain Computing, School of Automation Science and Electrical Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100451446","display_name":"Kexin Liu","orcid":"https://orcid.org/0000-0003-4328-6339"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kexin Liu","raw_affiliation_strings":["Beijing Advanced Innovation Center for Big Data and Brain Computing, School of Automation Science and Electrical Engineering, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-4328-6339","affiliations":[{"raw_affiliation_string":"Beijing Advanced Innovation Center for Big Data and Brain Computing, School of Automation Science and Electrical Engineering, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027725400","display_name":"Jinhu L\u00fc","orcid":"https://orcid.org/0000-0003-0275-8387"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinhu Lu","raw_affiliation_strings":["State Key Laboratory of Software Development Environment, School of Automation Science and Electrical Engineering, and the Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0003-0275-8387","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Software Development Environment, School of Automation Science and Electrical Engineering, and the Beijing Advanced Innovation Center for Big Data and Brain Computing, Beihang University, Beijing, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004170577"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":3.5627,"has_fulltext":false,"cited_by_count":35,"citation_normalized_percentile":{"value":0.9322559,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"67","issue":"12","first_page":"5268","last_page":"5280"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.9998999834060669,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.9994000196456909,"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/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9991999864578247,"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/synchronization","display_name":"Synchronization (alternating current)","score":0.7060679197311401},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6581785082817078},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.6180645823478699},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.609980046749115},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6048936247825623},{"id":"https://openalex.org/keywords/complex-network","display_name":"Complex network","score":0.47186702489852905},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4711519479751587},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4654655456542969},{"id":"https://openalex.org/keywords/stochastic-process","display_name":"Stochastic process","score":0.45505955815315247},{"id":"https://openalex.org/keywords/coupling","display_name":"Coupling (piping)","score":0.445287823677063},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33762869238853455},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.29671040177345276},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.1956537961959839},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0900094211101532},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08718472719192505},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07382789254188538}],"concepts":[{"id":"https://openalex.org/C2778562939","wikidata":"https://www.wikidata.org/wiki/Q1298791","display_name":"Synchronization (alternating current)","level":3,"score":0.7060679197311401},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6581785082817078},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.6180645823478699},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.609980046749115},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6048936247825623},{"id":"https://openalex.org/C34947359","wikidata":"https://www.wikidata.org/wiki/Q665189","display_name":"Complex network","level":2,"score":0.47186702489852905},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4711519479751587},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4654655456542969},{"id":"https://openalex.org/C8272713","wikidata":"https://www.wikidata.org/wiki/Q176737","display_name":"Stochastic process","level":2,"score":0.45505955815315247},{"id":"https://openalex.org/C131584629","wikidata":"https://www.wikidata.org/wiki/Q4308705","display_name":"Coupling (piping)","level":2,"score":0.445287823677063},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33762869238853455},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.29671040177345276},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.1956537961959839},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0900094211101532},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08718472719192505},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07382789254188538},{"id":"https://openalex.org/C136764020","wikidata":"https://www.wikidata.org/wiki/Q466","display_name":"World Wide Web","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcsi.2020.3020146","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcsi.2020.3020146","pdf_url":null,"source":{"id":"https://openalex.org/S116977442","display_name":"IEEE Transactions on Circuits and Systems I Regular Papers","issn_l":"1549-8328","issn":["1549-8328","1558-0806"],"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 Circuits and Systems I: Regular Papers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3523307272","display_name":null,"funder_award_id":"61621003","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3790558860","display_name":null,"funder_award_id":"2020TQ0027","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G5706247658","display_name":null,"funder_award_id":"61532020","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8258143549","display_name":null,"funder_award_id":"61903017","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W247697463","https://openalex.org/W261461018","https://openalex.org/W1488435683","https://openalex.org/W1494628843","https://openalex.org/W1509185796","https://openalex.org/W1576707917","https://openalex.org/W1630241696","https://openalex.org/W1964060135","https://openalex.org/W1966037807","https://openalex.org/W1979348722","https://openalex.org/W2005610185","https://openalex.org/W2032332507","https://openalex.org/W2034356849","https://openalex.org/W2038896449","https://openalex.org/W2063246107","https://openalex.org/W2065029123","https://openalex.org/W2068118500","https://openalex.org/W2069519093","https://openalex.org/W2070730311","https://openalex.org/W2072890207","https://openalex.org/W2090167557","https://openalex.org/W2099129142","https://openalex.org/W2100935517","https://openalex.org/W2104027563","https://openalex.org/W2123738293","https://openalex.org/W2134282505","https://openalex.org/W2142074197","https://openalex.org/W2166103243","https://openalex.org/W2167675176","https://openalex.org/W2241956900","https://openalex.org/W2262763250","https://openalex.org/W2283952362","https://openalex.org/W2293216767","https://openalex.org/W2351585786","https://openalex.org/W2484117929","https://openalex.org/W2521296520","https://openalex.org/W2528157742","https://openalex.org/W2529676626","https://openalex.org/W2555620376","https://openalex.org/W2765956954","https://openalex.org/W2773015394","https://openalex.org/W2801010298","https://openalex.org/W2905525468","https://openalex.org/W2943577819","https://openalex.org/W2946019601","https://openalex.org/W2948871169","https://openalex.org/W3100348600","https://openalex.org/W3210839039","https://openalex.org/W4238591275","https://openalex.org/W4285719527","https://openalex.org/W6681220702","https://openalex.org/W6762712973"],"related_works":["https://openalex.org/W2365689671","https://openalex.org/W2075004210","https://openalex.org/W1963981678","https://openalex.org/W1522710368","https://openalex.org/W3167551645","https://openalex.org/W2772733144","https://openalex.org/W2573473619","https://openalex.org/W1934622834","https://openalex.org/W3113498971","https://openalex.org/W2015036175"],"abstract_inverted_index":{"In":[0,18],"the":[1,21,26,54,118],"paper,":[2],"synchronization":[3,34,66,98],"of":[4,20,25,53,67,84,99],"nonlinear":[5,71],"dynamical":[6,101],"complex":[7,68,100],"networks":[8,69,102],"with":[9,50,70],"stochastic":[10,46,60,74],"coupling":[11,75],"under":[12],"adaptive":[13,32,85,93],"PI":[14,33,86,94],"control":[15,87,95],"is":[16],"considered.":[17],"light":[19],"relative":[22],"states":[23],"information":[24],"network":[27],"nodes,":[28],"node-":[29],"and":[30,38,62,73],"edge-based":[31],"protocols":[35,88,96],"are":[36,42,89,103,113],"proposed":[37,92],"several":[39],"sufficient":[40],"conditions":[41],"derived.":[43],"By":[44],"employing":[45],"analysis":[47],"techniques":[48],"combined":[49],"a":[51],"version":[52],"LaSalle's":[55],"invariant":[56],"principles":[57],"applied":[58],"to":[59,116],"process":[61],"Lyapunov":[63],"function":[64],"approaches,":[65],"dynamics":[72],"reaches":[76],"in":[77],"mean":[78],"square":[79],"via":[80],"these":[81],"two":[82],"types":[83],"proved.":[90],"The":[91],"for":[97,105],"useful":[104],"future":[106],"realistic":[107],"engineering":[108],"systems":[109],"design.":[110],"Numerical":[111],"examples":[112],"finally":[114],"simulated":[115],"validate":[117],"theoretical":[119],"analysis.":[120]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":4}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}
