{"id":"https://openalex.org/W2289883144","doi":"https://doi.org/10.1109/cdc.2015.7403330","title":"Backstepping PDE design, Volterra and Fredholm operators: A convex optimization approach","display_name":"Backstepping PDE design, Volterra and Fredholm operators: A convex optimization approach","publication_year":2015,"publication_date":"2015-12-01","ids":{"openalex":"https://openalex.org/W2289883144","doi":"https://doi.org/10.1109/cdc.2015.7403330","mag":"2289883144"},"language":"en","primary_location":{"id":"doi:10.1109/cdc.2015.7403330","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7403330","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"conference-paper","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/A5029328828","display_name":"Pedro Ascencio","orcid":"https://orcid.org/0000-0002-7837-9001"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Pedro Ascencio","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, SW7 2AZ, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, SW7 2AZ, U.K","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5018225150","display_name":"Alessandro Astolfi","orcid":"https://orcid.org/0000-0002-4331-454X"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Alessandro Astolfi","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, SW7 2AZ, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, SW7 2AZ, U.K","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013370088","display_name":"Thomas Parisini","orcid":"https://orcid.org/0000-0001-5396-9665"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Thomas Parisini","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, Imperial College London, SW7 2AZ, U.K"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, Imperial College London, SW7 2AZ, U.K","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"7048","last_page":"7053"},"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":0.9995999932289124,"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":0.9995999932289124,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9940999746322632,"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/mathematics","display_name":"Mathematics","score":0.7522858381271362},{"id":"https://openalex.org/keywords/semidefinite-programming","display_name":"Semidefinite programming","score":0.6137441992759705},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5142363905906677},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.5089364051818848},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.4867398738861084},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.45733246207237244},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.4338001608848572},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.4304143190383911},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39597076177597046},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37136903405189514},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.35097557306289673},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.34311795234680176},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1861571967601776}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7522858381271362},{"id":"https://openalex.org/C101901036","wikidata":"https://www.wikidata.org/wiki/Q2269096","display_name":"Semidefinite programming","level":2,"score":0.6137441992759705},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5142363905906677},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5089364051818848},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.4867398738861084},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.45733246207237244},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.4338001608848572},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.4304143190383911},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39597076177597046},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37136903405189514},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.35097557306289673},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.34311795234680176},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1861571967601776},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc.2015.7403330","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc.2015.7403330","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2015 54th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:arts.units.it:11368/2851520","is_oa":false,"landing_page_url":"http://hdl.handle.net/11368/2851520","pdf_url":null,"source":{"id":"https://openalex.org/S4306400480","display_name":"ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I142444530","host_organization_name":"University of Trieste","host_organization_lineage":["https://openalex.org/I142444530"],"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":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W563110697","https://openalex.org/W585700782","https://openalex.org/W653291882","https://openalex.org/W1498121547","https://openalex.org/W1559197676","https://openalex.org/W1587708275","https://openalex.org/W1966249877","https://openalex.org/W1988178552","https://openalex.org/W2060819023","https://openalex.org/W2074911531","https://openalex.org/W2094218171","https://openalex.org/W2119967247","https://openalex.org/W2536620281"],"related_works":["https://openalex.org/W2972080159","https://openalex.org/W2017640945","https://openalex.org/W2031473926","https://openalex.org/W2386739836","https://openalex.org/W2493083010","https://openalex.org/W2021616187","https://openalex.org/W4308895501","https://openalex.org/W22811207","https://openalex.org/W2189527329","https://openalex.org/W2397046274"],"abstract_inverted_index":{"This":[0],"paper":[1],"deals":[2],"with":[3],"backstepping":[4],"design":[5],"for":[6,22,64],"boundary":[7],"PDE":[8],"control/observer":[9],"as":[10,78],"a":[11,23,83],"convex":[12],"optimization":[13],"problem.":[14,87],"Both":[15],"Volterra":[16],"and":[17,27,50,56,85],"Fredholm":[18],"operators":[19],"are":[20,33,44,62,76],"analysed":[21],"class":[24],"of":[25,37,42,58,70,82,90],"parabolic":[26],"hyperbolic":[28],"PDEs.":[29],"The":[30,73,88],"resulting":[31],"Kernel-PDEs":[32],"formulated":[34],"in":[35,67],"terms":[36],"polynomial":[38,65],"functions,":[39],"the":[40,59,68,79],"parameters":[41],"which":[43],"optimized":[45],"using":[46],"Sum-of-Squares":[47],"(SOS)":[48],"techniques":[49],"solved":[51],"via":[52],"semidefinite":[53],"programming.":[54],"Uniqueness":[55],"invertibility":[57],"Fredholm-type":[60],"transformation":[61],"proven":[63],"Kernels":[66],"space":[69],"real-analytic":[71],"functions.":[72],"inverse":[74],"kernels":[75],"approximated":[77],"optimal":[80],"solution":[81],"SOS":[84],"moment":[86],"effectiveness":[89],"this":[91],"approach":[92],"is":[93],"illustrated":[94],"by":[95],"numerical":[96],"simulations.":[97]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}
