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...
Guardado en:
| Autores principales: | , , |
|---|---|
| Lenguaje: | English |
| Publicado: |
Universidad Católica del Norte, Departamento de Matemáticas
2010
|
| Materias: | |
| Acceso en línea: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000200007 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | 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. |
|---|