Ayse Kara: Controllability Property of Affine Systems on some Lie Groups

Let G be a connected Lie group and L(G) be its Lie algebra. An
afine control system $\Sigma=(G,D)$ is defined by the specification of
the following data : $g=(X+D)_g+\sum_{j=1}^d u_j(t)(Y^j+D^j)_g$ where
$g\in G$, $X,Y^1,Y^2,...,Y^d\in L(G)$, $D,D^1,D^2,,,.D^d\in
\partial(L(G))$ and $u_j$ are controls. Controllabilityproblem is to
reach each point of the state space which is our connected Lie group by
the vector fields parametrized by controls of the dynamic, strategies,
with the positive time. In this talk, controllability problem is studied
related to its associated bilinear part of the system. The fundamental
result is on Euclidean space of dimension n by Jurdjevic and Sallet, and
then there exist extensions to Generalized Heisenberg Lie groups and
Carnot Groups.

The talk will start a general presentation of control theory at the
first hour.