Publicação
Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
| Resumo: | We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results. |
|---|---|
| Autores principais: | Karite, Touria |
| Outros Autores: | Khazari, Adil; Torres, Delfim F. M. |
| Assunto: | Regional controllability Fractional-order systems Caputo derivatives Control delays Optimal control Minimum energy |
| Ano: | 2022 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade de Aveiro |
| Idioma: | inglês |
| Origem: | RIA - Repositório Institucional da Universidade de Aveiro |
| _version_ | 1866173072738877440 |
|---|---|
| author | Karite, Touria |
| author2 | Khazari, Adil Torres, Delfim F. M. |
| author2_role | author author |
| author_facet | Karite, Touria Khazari, Adil Torres, Delfim F. M. |
| author_role | author |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Karite, Touria\"},{\"Person.name\":\"Khazari, Adil\"},{\"Person.name\":\"Torres, Delfim F. M.\"}] |
| datacite.creators.creator.creatorName.fl_str_mv | Karite, Touria Khazari, Adil Torres, Delfim F. M. |
| datacite.date.Accepted.fl_str_mv | 2022-12-18T00:00:00Z |
| datacite.date.available.fl_str_mv | 2022-12-22T16:47:57Z |
| datacite.date.embargoed.fl_str_mv | 2022-12-22T16:47:57Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Regional controllability Fractional-order systems Caputo derivatives Control delays Optimal control Minimum energy |
| datacite.titles.title.fl_str_mv | Regional controllability and minimum energy control of delayed caputo fractional-order linear systems |
| dc.creator.none.fl_str_mv | Karite, Touria Khazari, Adil Torres, Delfim F. M. |
| dc.date.Accepted.fl_str_mv | 2022-12-18T00:00:00Z |
| dc.date.available.fl_str_mv | 2022-12-22T16:47:57Z |
| dc.date.embargoed.fl_str_mv | 2022-12-22T16:47:57Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10773/35547 |
| dc.language.none.fl_str_mv | eng |
| dc.publisher.none.fl_str_mv | MDPI |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Regional controllability Fractional-order systems Caputo derivatives Control delays Optimal control Minimum energy |
| dc.title.fl_str_mv | Regional controllability and minimum energy control of delayed caputo fractional-order linear systems |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| id | ria_fd2fc4e4e1462ebb3119f91c243854f2 |
| identifier.url.fl_str_mv | http://hdl.handle.net/10773/35547 |
| instacron_str | ua |
| institution | Universidade de Aveiro |
| instname_str | Universidade de Aveiro |
| language | eng |
| network_acronym_str | ria |
| network_name_str | RIA - Repositório Institucional da Universidade de Aveiro |
| oai_identifier_str | oai:ria.ua.pt:10773/35547 |
| organization_str_mv | urn:organizationAcronym:ua |
| person_str_mv | Karite, Touria Khazari, Adil Torres, Delfim F. M. |
| publishDate | 2022 |
| publisher.none.fl_str_mv | MDPI |
| reponame_str | RIA - Repositório Institucional da Universidade de Aveiro |
| repository_id_str | urn:repositoryAcronym:ria |
| service_str_mv | urn:repositoryAcronym:ria |
| spelling | pt_PTWe study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results.application/pdfengMDPIpt_PTRegional controllability and minimum energy control of delayed caputo fractional-order linear systemsKarite, TouriaKhazari, AdilTorres, Delfim F. M.Handlehttp://hdl.handle.net/10773/35547ISSNIsPartOf2227-7390DOIIsPartOf10.3390/math102448132022-12-22T16:47:57Z2022-12-18T00:00:00Z2022-12-18http://purl.org/coar/access_right/c_abf2open accesspt_PTRegional controllabilitypt_PTFractional-order systemspt_PTCaputo derivativespt_PTControl delayspt_PTOptimal controlpt_PTMinimum energy340953 byteshttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://ria.ua.pt/bitstream/10773/35547/1/%5b523%5dKarite-Khazari-Torres.pdfliteraturehttp://purl.org/coar/resource_type/c_6501journal article |
| spellingShingle | Regional controllability and minimum energy control of delayed caputo fractional-order linear systems Karite, Touria Regional controllability Fractional-order systems Caputo derivatives Control delays Optimal control Minimum energy |
| status | SINGLETON |
| subject.fl_str_mv | Regional controllability Fractional-order systems Caputo derivatives Control delays Optimal control Minimum energy |
| title | Regional controllability and minimum energy control of delayed caputo fractional-order linear systems |
| title_full | Regional controllability and minimum energy control of delayed caputo fractional-order linear systems |
| title_fullStr | Regional controllability and minimum energy control of delayed caputo fractional-order linear systems |
| title_full_unstemmed | Regional controllability and minimum energy control of delayed caputo fractional-order linear systems |
| title_short | Regional controllability and minimum energy control of delayed caputo fractional-order linear systems |
| title_sort | Regional controllability and minimum energy control of delayed caputo fractional-order linear systems |
| topic | Regional controllability Fractional-order systems Caputo derivatives Control delays Optimal control Minimum energy |
| topic_facet | Regional controllability Fractional-order systems Caputo derivatives Control delays Optimal control Minimum energy |
| url | http://hdl.handle.net/10773/35547 |
| visible | 1 |