Publicación:
Geometric numerical methods for Lie systems and their application in optimal control

Vista sencilla de ítem
dc.contributor.authorBlanco Díaz, Luis
dc.contributor.authorSardón, Cristina
dc.contributor.authorJiménez Alburquerque, Fernando
dc.contributor.authorLucas, Javier de
dc.date.accessioned2026-01-19T17:10:20Z
dc.date.available2026-01-19T17:10:20Z
dc.date.issued2023-06-19
dc.descriptionThe registered version of this article, first published in Symmetry, is available online at the publisher's website: MDPI, https://doi.org/10.3390/sym15061285
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en Symmetry, está disponible en línea en el sitio web del editor: MDPI, https://doi.org/10.3390/sym15061285
dc.description.abstractA Lie system is a nonautonomous system of first-order ordinary differential equations whose general solution can be written via an autonomous function, the so-called (nonlinear) superposition rule of a finite number of particular solutions and some parameters to be related to initial conditions. This superposition rule can be obtained using the geometric features of the Lie system, its symmetries, and the symmetric properties of certain morphisms involved. Even if a superposition rule for a Lie system is known, the explicit analytic expression of its solutions frequently is not. This is why this article focuses on a novel geometric attempt to integrate Lie systems analytically and numerically. We focus on two families of methods based on Magnus expansions and on Runge–Kutta–Munthe–Kaas methods, which are here adapted, in a geometric manner, to Lie systems. To illustrate the accuracy of our techniques we analyze Lie systems related to Lie groups of the form SL(𝑛,ℝ) , which play a very relevant role in mechanics. In particular, we depict an optimal control problem for a vehicle with quadratic cost function. Particular numerical solutions of the studied examples are given.en
dc.description.provenanceMade available in DSpace on 2026-01-19T17:10:20Z (GMT). No. of bitstreams: 1 Geometric numerical methods for Lie systems and their application in optimal control.pdf: 506702 bytes, checksum: 5544102520878a581ea2755718d84065 (MD5) Previous issue date: 2023-06-19en
dc.description.versionversión publicada
dc.identifier.citationBlanco Díaz, L., Sardón, C., Jiménez Alburquerque, F., & de Lucas, J. (2023). Geometric Numerical Methods for Lie Systems and Their Application in Optimal Control. Symmetry, 15(6). https://doi.org/10.3390/SYM15061285
dc.identifier.doihttps://doi.org/10.3390/sym15061285
dc.identifier.eissn2073-8994
dc.identifier.issn.
dc.identifier.urihttps://hdl.handle.net/20.500.14468/31468
dc.journal.issue6
dc.journal.titleSymmetry
dc.journal.volume15
dc.language.isoen
dc.publisherMDPI
dc.relation.centerE.T.S. de Ingenieros Industriales
dc.relation.departmentMatemática Aplicada I
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.es
dc.subject12 Matemáticas
dc.subject.keywordsLie group integrationen
dc.subject.keywordsgeometric numerical methodsen
dc.subject.keywordsnumerical methods for Lie systemsen
dc.titleGeometric numerical methods for Lie systems and their application in optimal controlen
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
relation.isAuthorOfPublication2e39e62c-a93f-46b7-aa64-7b2227e7a2dd
relation.isAuthorOfPublication.latestForDiscovery2e39e62c-a93f-46b7-aa64-7b2227e7a2dd
Archivos
Bloque original
Mostrando 1 - 1 de 1
Miniatura
Nombre:
Geometric numerical methods for Lie systems and their application in optimal control.pdf
Tamaño:
494.83 KB
Formato:
Adobe Portable Document Format
Descargar
Bloque de licencias
Mostrando 1 - 1 de 1
No hay miniatura disponible
Nombre:
license.txt
Tamaño:
3.62 KB
Formato:
Item-specific license agreed to upon submission
Descripción:
Descargar
Colecciones
Artículos y papers