Equivalence of Control Systems with Linear Systems on Lie Groups and Homogeneous Spaces
| dc.creator | Jouan, Philippe | |
| dc.date | 2008-11-29 | |
| dc.date.accessioned | 2026-07-07T12:08:07Z | |
| dc.date.available | 2026-07-07T12:08:07Z | |
| dc.description | The aim of this paper is to prove that a control affine system on a manifold is equivalent by diffeomorphism to a linear system on a Lie group or a homogeneous space if and only the vector fields of the system are complete and generate a finite dimensional Lie algebra. A vector field on a connected Lie group is linear if its flow is a one parameter group of automorphisms. An affine vector field is obtained by adding a left invariant one. Its projection on a homogeneous space, whenever it exists, is still called affine. Affine vector fields on homogeneous spaces can be characterized by their Lie brackets with the projections of right invariant vector fields. A linear system on a homogeneous space is a system whose drift part is affine and whose controlled part is invariant. The main result is based on a general theorem on finite dimensional algebras generated by complete vector fields, closely related to a theorem of Palais, and which have its own interest. The present proof makes use of geometric control theory arguments. | |
| dc.identifier | https://arxiv.org/abs/0812.0058 | |
| dc.identifier | http://arxiv.org/abs/0812.0058 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/209207 | |
| dc.subject | Optimization and Control | |
| dc.subject | Differential Geometry | |
| dc.title | Equivalence of Control Systems with Linear Systems on Lie Groups and Homogeneous Spaces | |
| dc.type | text |