{"id":"https://openalex.org/W3039802226","doi":"https://doi.org/10.1109/lcsys.2020.3003514","title":"Robust Control Design of Underactuated 2 \u00d7 2 PDE-ODE-PDE Systems","display_name":"Robust Control Design of Underactuated 2 \u00d7 2 PDE-ODE-PDE Systems","publication_year":2020,"publication_date":"2020-06-18","ids":{"openalex":"https://openalex.org/W3039802226","doi":"https://doi.org/10.1109/lcsys.2020.3003514","mag":"3039802226"},"language":"en","primary_location":{"id":"doi:10.1109/lcsys.2020.3003514","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2020.3003514","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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 Control Systems Letters","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-02931065","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007129316","display_name":"Jean Auriol","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean Auriol","raw_affiliation_strings":["Universit&#x00E9; Paris-Saclay, CNRS, CentraleSup&#x00E9;lec, Laboratoire des signaux et syst&#x00E8;mes, Gif-sur-Yvette, France","L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)"],"affiliations":[{"raw_affiliation_string":"Universit&#x00E9; Paris-Saclay, CNRS, CentraleSup&#x00E9;lec, Laboratoire des signaux et syst&#x00E8;mes, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210097418","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210097418"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000114606","display_name":"Ulf Jakob F. Aarsnes","orcid":null},"institutions":[{"id":"https://openalex.org/I4210107808","display_name":"NORCE Research AS","ror":"https://ror.org/02gagpf75","country_code":"NO","type":"facility","lineage":["https://openalex.org/I4210107808"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Ulf Jakob F. Aarsnes","raw_affiliation_strings":["NORCE, Norwegian Research Centre AS, Oslo, Norway"],"affiliations":[{"raw_affiliation_string":"NORCE, Norwegian Research Centre AS, Oslo, Norway","institution_ids":["https://openalex.org/I4210107808"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008065595","display_name":"Florent Di Meglio","orcid":null},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Florent Di Meglio","raw_affiliation_strings":["Centre Automatique et Syst\u00e8mes, Mines ParisTech, PSL Research University, Paris, France","CAS - Centre Automatique et Syst\u00e8mes (35 rue Saint-Honor\u00e9 77305 Fontainebleau cedex - France)"],"affiliations":[{"raw_affiliation_string":"Centre Automatique et Syst\u00e8mes, Mines ParisTech, PSL Research University, Paris, France","institution_ids":["https://openalex.org/I70768539","https://openalex.org/I2746051580"]},{"raw_affiliation_string":"CAS - Centre Automatique et Syst\u00e8mes (35 rue Saint-Honor\u00e9 77305 Fontainebleau cedex - France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045063201","display_name":"Roman Shor","orcid":null},"institutions":[{"id":"https://openalex.org/I168635309","display_name":"University of Calgary","ror":"https://ror.org/03yjb2x39","country_code":"CA","type":"education","lineage":["https://openalex.org/I168635309"]},{"id":"https://openalex.org/I252914616","display_name":"BP (Canada)","ror":"https://ror.org/051177492","country_code":"CA","type":"company","lineage":["https://openalex.org/I20303223","https://openalex.org/I252914616"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Roman Shor","raw_affiliation_strings":["Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, AB, Canada","Department of Chemical and Petroleum Engineering [Calgary] (Calgary, AB T2N 1N4 - Canada)"],"affiliations":[{"raw_affiliation_string":"Department of Chemical and Petroleum Engineering, University of Calgary, Calgary, AB, Canada","institution_ids":["https://openalex.org/I168635309"]},{"raw_affiliation_string":"Department of Chemical and Petroleum Engineering [Calgary] (Calgary, AB T2N 1N4 - Canada)","institution_ids":["https://openalex.org/I252914616"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5007129316"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I4210097418"],"apc_list":null,"apc_paid":null,"fwci":1.1769,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78320562,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"5","issue":"2","first_page":"469","last_page":"474"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","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/T11110","display_name":"Stability and Controllability of Differential Equations","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/T11416","display_name":"Numerical methods for differential equations","score":0.9914000034332275,"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":0.9801999926567078,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/backstepping","display_name":"Backstepping","score":0.9397072792053223},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.8691115379333496},{"id":"https://openalex.org/keywords/underactuation","display_name":"Underactuation","score":0.8478890657424927},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.6990231275558472},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.6454285383224487},{"id":"https://openalex.org/keywords/controller","display_name":"Controller (irrigation)","score":0.478211373090744},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4774530529975891},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.4354398548603058},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42070767283439636},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.37974873185157776},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2517046332359314},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.24442517757415771},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21927398443222046},{"id":"https://openalex.org/keywords/adaptive-control","display_name":"Adaptive control","score":0.14449119567871094}],"concepts":[{"id":"https://openalex.org/C72218879","wikidata":"https://www.wikidata.org/wiki/Q4839759","display_name":"Backstepping","level":4,"score":0.9397072792053223},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8691115379333496},{"id":"https://openalex.org/C88337583","wikidata":"https://www.wikidata.org/wiki/Q7883433","display_name":"Underactuation","level":3,"score":0.8478890657424927},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.6990231275558472},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.6454285383224487},{"id":"https://openalex.org/C203479927","wikidata":"https://www.wikidata.org/wiki/Q5165939","display_name":"Controller (irrigation)","level":2,"score":0.478211373090744},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4774530529975891},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.4354398548603058},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42070767283439636},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.37974873185157776},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2517046332359314},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.24442517757415771},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21927398443222046},{"id":"https://openalex.org/C107464732","wikidata":"https://www.wikidata.org/wiki/Q235781","display_name":"Adaptive control","level":3,"score":0.14449119567871094},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C6557445","wikidata":"https://www.wikidata.org/wiki/Q173113","display_name":"Agronomy","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/lcsys.2020.3003514","is_oa":false,"landing_page_url":"https://doi.org/10.1109/lcsys.2020.3003514","pdf_url":null,"source":{"id":"https://openalex.org/S4306422535","display_name":"IEEE Control Systems Letters","issn_l":"2475-1456","issn":["2475-1456"],"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 Control Systems Letters","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02931065v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02931065","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"IEEE Control Systems Letters, 2021, 5 (2), pp.469-474. &#x27E8;10.1109/lcsys.2020.3003514&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02931065v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02931065","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"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":"IEEE Control Systems Letters, 2021, 5 (2), pp.469-474. &#x27E8;10.1109/lcsys.2020.3003514&#x27E9;","raw_type":"Journal articles"},"sustainable_development_goals":[{"score":0.7400000095367432,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1546613882","https://openalex.org/W1555627060","https://openalex.org/W1607633954","https://openalex.org/W1966853343","https://openalex.org/W1990834757","https://openalex.org/W1991059830","https://openalex.org/W2021731075","https://openalex.org/W2058945808","https://openalex.org/W2121454958","https://openalex.org/W2178205091","https://openalex.org/W2400848186","https://openalex.org/W2482021336","https://openalex.org/W2529757039","https://openalex.org/W2803813664","https://openalex.org/W2808930339","https://openalex.org/W2809066356","https://openalex.org/W2810955800","https://openalex.org/W2915004578","https://openalex.org/W2917580745","https://openalex.org/W2963591151","https://openalex.org/W2972350237","https://openalex.org/W2973096083","https://openalex.org/W3012361552","https://openalex.org/W3012460068","https://openalex.org/W4211202937"],"related_works":["https://openalex.org/W2771027241","https://openalex.org/W1765905465","https://openalex.org/W2793080664","https://openalex.org/W3206152082","https://openalex.org/W2500162090","https://openalex.org/W2046770915","https://openalex.org/W2217718355","https://openalex.org/W3205444542","https://openalex.org/W1498122250","https://openalex.org/W2099991058"],"abstract_inverted_index":{"In":[0],"this":[1,82],"letter,":[2],"we":[3,92],"design":[4,57,94],"a":[5,10,40,60,86],"robust":[6],"stabilizing":[7],"controller":[8],"for":[9,90],"system":[11,44,67,84,89],"composed":[12],"of":[13,16,26,28,50],"two":[14],"sets":[15],"linear":[17],"heterodirectional":[18],"hyperbolic":[19],"PDEs,":[20,30],"with":[21,37],"actuation":[22,75],"at":[23,33],"one":[24,27,49],"boundary":[25,36,72],"the":[29,34,51,65,70,74],"and":[31],"couplings":[32,68],"middle":[35],"ODEs":[38],"in":[39],"PDE-ODE-PDE":[41],"configuration.":[42],"The":[43,56],"is":[45,54,76],"underactuated":[46],"since":[47],"only":[48],"PDE":[52],"systems":[53],"actuated.":[55],"approach":[58],"employs":[59],"backstepping":[61],"transformation":[62],"to":[63,69,99],"move":[64],"undesired":[66],"proximal":[71],"(where":[73],"located).":[77],"We":[78],"can":[79,93],"then":[80],"express":[81],"target":[83,104],"as":[85],"time-delay":[87],"neutral":[88],"which":[91],"an":[95,101],"appropriate":[96],"control":[97],"law":[98],"obtain":[100],"exponentially":[102],"stable":[103],"system.":[105]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1}],"updated_date":"2026-01-28T23:14:49.684275","created_date":"2025-10-10T00:00:00"}
