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Extremals of a quadratic cost optimal problem on the real projective line.

dc.creatorAyala, Víctor
dc.creatorRodríguez, Juan Carlos
dc.creatorSan Martín, Luiz A. B.
dc.date2010-08-07
dc.identifierhttps://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1206
dc.identifier10.4067/S0716-09172010000200007
dc.descriptionLet Σ be a bilinear control system on R2 whose matrices generate the Lie algebra sl(2) of the Lie group Sl(2) : the group of order two real matrices with determinant 1. In this work we focus on the extremals of a quadratic cost optimal problem for the angle system PΣ defined by the projection of Σ onto the real projective line P1. It has been proved in [2] that through the Cartan-Killing form the cotangent bundle of P1 can be identified with a cone C in sl(2). Via the Pontryagin Maximum Principle, we explicitly show the extremals by using the mentioned identification and the special form of the trajectories associated with the lifting of vector fields on PΣ. We analyze both: the controllable case and when the system bf P Σ give rise to control sets. Some examples are shown.es-ES
dc.formatapplication/pdf
dc.languageeng
dc.publisherUniversidad Católica del Norte.en-US
dc.relationhttps://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1206/1080
dc.rightsCopyright (c) 2010 Proyecciones. Journal of Mathematicsen-US
dc.rightshttp://creativecommons.org/licenses/by/4.0en-US
dc.sourceProyecciones (Antofagasta, On line); Vol. 29 No. 2 (2010); 145-164en-US
dc.sourceProyecciones. Revista de Matemática; Vol. 29 Núm. 2 (2010); 145-164es-ES
dc.source0717-6279
dc.subjectOptimal control problemes-ES
dc.subjectextremalses-ES
dc.subjectPontryagin maximum principlees-ES
dc.subjectbilinear control systemses-ES
dc.subjectangle systemes-ES
dc.subjectCartan-Killing formes-ES
dc.subjectreal projective linees-ES
dc.subjectspecial linear Lie groupes-ES
dc.subjectproblema del control óptimoes-ES
dc.subjectextremoses-ES
dc.subjectprincipio del máximo de Pontryagin.es-ES
dc.titleExtremals of a quadratic cost optimal problem on the real projective line.es-ES
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/publishedVersion
dc.typePeer-reviewed Articleen-US


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