EXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINE

Let S 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 PSdefined by the projection of S on...

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Autores principales:	Ayala,V, Rodríguez,J. C, San Martín,L. A. B
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2010
Materias:	optimal control problem extremals Pontryagin maximum principle bilinear control systems angle system Cartan-Killing form real projective line special linear Lie group
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000200007
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spelling	oai:scielo:S0716-091720100002000072014-08-14EXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINEAyala,VRodríguez,J. CSan Martín,L. A. B optimal control problem extremals Pontryagin maximum principle bilinear control systems angle system Cartan-Killing form real projective line special linear Lie group Let S 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 PSdefined by the projection of S 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 PS. We analyze both: the controllable case and when the system bf P S give rise to control sets. Some examples are shown.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.29 n.2 20102010-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000200007en10.4067/S0716-09172010000200007
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	optimal control problem extremals Pontryagin maximum principle bilinear control systems angle system Cartan-Killing form real projective line special linear Lie group
spellingShingle	optimal control problem extremals Pontryagin maximum principle bilinear control systems angle system Cartan-Killing form real projective line special linear Lie group Ayala,V Rodríguez,J. C San Martín,L. A. B EXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINE
description	Let S 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 PSdefined by the projection of S 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 PS. We analyze both: the controllable case and when the system bf P S give rise to control sets. Some examples are shown.
author	Ayala,V Rodríguez,J. C San Martín,L. A. B
author_facet	Ayala,V Rodríguez,J. C San Martín,L. A. B
author_sort	Ayala,V
title	EXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINE
title_short	EXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINE
title_full	EXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINE
title_fullStr	EXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINE
title_full_unstemmed	EXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINE
title_sort	extremals of a quadratic cost optimal problem on the real projective line
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2010
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000200007
work_keys_str_mv	AT ayalav extremalsofaquadraticcostoptimalproblemontherealprojectiveline AT rodriguezjc extremalsofaquadraticcostoptimalproblemontherealprojectiveline AT sanmartinlab extremalsofaquadraticcostoptimalproblemontherealprojectiveline
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EXTREMALS OF A QUADRATIC COST OPTIMAL PROBLEM ON THE REAL PROJECTIVE LINE

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