A recursive LMI-based algorithm for efficient vertex reduction in LPV systems

This paper proposes a new algorithm to reduce the number of gains of a polytopic LPV controller considering generic tuples of vertices, for which a common controller gain can be used. The use of Frobenius norm and the inclusion of the input matrix in the LMIs perturbation matrix allows decreasing th...

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Autores: Sanjuan Gómez, Adrián, Rotondo, Damiano|||0000-0002-8855-5582, Nejjari Akhi-Elarab, Fatiha|||0000-0001-9118-632X, Sarrate Estruch, Ramon|||0000-0002-9979-5899
Formato: artículo
Fecha de publicación:2021
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/362454
Acesso em linha:https://hdl.handle.net/2117/362454
https://dx.doi.org/10.1080/00207179.2021.1973682
Access Level:acceso abierto
Palavra-chave:System theory
Mathematical models
Predictive control
Linear parameter varying (LPV)
Linear matrix inequalities (LMIs)
Vertex reduction
State-feedback control
Sistemes, Teoria de
Models matemàtics
Control predictiu
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
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oai_identifier_str oai:upcommons.upc.edu:2117/362454
network_acronym_str ES
network_name_str España
repository_id_str
spelling A recursive LMI-based algorithm for efficient vertex reduction in LPV systemsSanjuan Gómez, AdriánRotondo, Damiano|||0000-0002-8855-5582Nejjari Akhi-Elarab, Fatiha|||0000-0001-9118-632XSarrate Estruch, Ramon|||0000-0002-9979-5899System theoryMathematical modelsPredictive controlLinear parameter varying (LPV)Linear matrix inequalities (LMIs)Vertex reductionState-feedback controlSistemes, Teoria deModels matemàticsControl predictiuÀrees temàtiques de la UPC::Informàtica::Automàtica i controlThis paper proposes a new algorithm to reduce the number of gains of a polytopic LPV controller considering generic tuples of vertices, for which a common controller gain can be used. The use of Frobenius norm and the inclusion of the input matrix in the LMIs perturbation matrix allows decreasing the conservativeness to select vertices which are combinable, with respect to a previous approach based on Gershgorin circles. A combinability metric that can be applied to an arbitrary partition of the set of vertices is defined. Then, a recursive algorithm finds a lesser-fragmented combinable partition at each iteration by combining together two elements of a partition. The algorithm aims at finding combinable partitions with minimal cardinality in fewer attempts, always preserving the original control performance specifications. The proposed method is validated using numerical examples, a twin rotor MIMO system and a two-link robotic manipulator.This work has been co-financed by the Spanish State Research Agency (AEI) and the European Regional Development Fund (ERFD) through the project SCAV (ref. MINECO DPI2017-88403-R), by the European Regional Development Fund of the European Union in the framework of the ERDF Operational Program of Catalonia 2014-2020 (ref. 001-P-001643 Looming Factory) and by the DGR of Generalitat de Catalunya (SAC group ref. 2017/SGR/482).Peer Reviewed20212021-01-0120222022-02-16journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/362454https://dx.doi.org/10.1080/00207179.2021.1973682reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/3624542026-05-27T15:37:01Z
dc.title.none.fl_str_mv A recursive LMI-based algorithm for efficient vertex reduction in LPV systems
title A recursive LMI-based algorithm for efficient vertex reduction in LPV systems
spellingShingle A recursive LMI-based algorithm for efficient vertex reduction in LPV systems
Sanjuan Gómez, Adrián
System theory
Mathematical models
Predictive control
Linear parameter varying (LPV)
Linear matrix inequalities (LMIs)
Vertex reduction
State-feedback control
Sistemes, Teoria de
Models matemàtics
Control predictiu
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
title_short A recursive LMI-based algorithm for efficient vertex reduction in LPV systems
title_full A recursive LMI-based algorithm for efficient vertex reduction in LPV systems
title_fullStr A recursive LMI-based algorithm for efficient vertex reduction in LPV systems
title_full_unstemmed A recursive LMI-based algorithm for efficient vertex reduction in LPV systems
title_sort A recursive LMI-based algorithm for efficient vertex reduction in LPV systems
dc.creator.none.fl_str_mv Sanjuan Gómez, Adrián
Rotondo, Damiano|||0000-0002-8855-5582
Nejjari Akhi-Elarab, Fatiha|||0000-0001-9118-632X
Sarrate Estruch, Ramon|||0000-0002-9979-5899
author Sanjuan Gómez, Adrián
author_facet Sanjuan Gómez, Adrián
Rotondo, Damiano|||0000-0002-8855-5582
Nejjari Akhi-Elarab, Fatiha|||0000-0001-9118-632X
Sarrate Estruch, Ramon|||0000-0002-9979-5899
author_role author
author2 Rotondo, Damiano|||0000-0002-8855-5582
Nejjari Akhi-Elarab, Fatiha|||0000-0001-9118-632X
Sarrate Estruch, Ramon|||0000-0002-9979-5899
author2_role author
author
author
dc.subject.none.fl_str_mv System theory
Mathematical models
Predictive control
Linear parameter varying (LPV)
Linear matrix inequalities (LMIs)
Vertex reduction
State-feedback control
Sistemes, Teoria de
Models matemàtics
Control predictiu
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
topic System theory
Mathematical models
Predictive control
Linear parameter varying (LPV)
Linear matrix inequalities (LMIs)
Vertex reduction
State-feedback control
Sistemes, Teoria de
Models matemàtics
Control predictiu
Àrees temàtiques de la UPC::Informàtica::Automàtica i control
description This paper proposes a new algorithm to reduce the number of gains of a polytopic LPV controller considering generic tuples of vertices, for which a common controller gain can be used. The use of Frobenius norm and the inclusion of the input matrix in the LMIs perturbation matrix allows decreasing the conservativeness to select vertices which are combinable, with respect to a previous approach based on Gershgorin circles. A combinability metric that can be applied to an arbitrary partition of the set of vertices is defined. Then, a recursive algorithm finds a lesser-fragmented combinable partition at each iteration by combining together two elements of a partition. The algorithm aims at finding combinable partitions with minimal cardinality in fewer attempts, always preserving the original control performance specifications. The proposed method is validated using numerical examples, a twin rotor MIMO system and a two-link robotic manipulator.
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-01-01
2022
2022-02-16
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/362454
https://dx.doi.org/10.1080/00207179.2021.1973682
url https://hdl.handle.net/2117/362454
https://dx.doi.org/10.1080/00207179.2021.1973682
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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