On properties of linear control systems on Lie groups

In this work we study controllability properties of linear control systems on Lie groups as introduced by Ayala and Tirao in [AT99]. A linear control system _x0006_Σ Lie group G is defined by x' = X(x) + Σ^k_j=1 u_jY_j(x), where the drift vector field X is an infinitesimal automorphism, u_j are piecewise constant functions, and the control vectors Y_j are left-invariant vector fields. Properties for the flow of the infinitesimal automorphism X and for the reachable set defined by _x0006_Σ are presented in Chapter 3. Under a condition similar to the Kalman condition which is needed for controllability of linear control systems on Rⁿ, Ayala and Tirao showed local controllability of the system Σ _x0006_at the group identity e. An alternate proof of this result is obtained using the Lie theory of semigroups. More importantly, an extension of this result is proved. These results are contained in Chapter 4. Finally, in Chapter 5 an example on the Heisenberg Lie group is presented and its properties are proved using the theory developed.

Name thesis:degree_name

Doctor of Philosophy (PhD)

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Applied Mathematics

Grantor

Mathematics

Year dc:date.available

2002

Author dc:creator

• Cardetti, Fabiana

• geometric control theory

Statement dc:rights

• unrestricted
• Release the entire work immediately for access worldwide.

Identifier

etd-0711102-152933
https://repository.lsu.edu/gradschool_dissertations/1074

OAI identifier oai:identifier

oai:repository.lsu.edu:gradschool_dissertations-2073