  Let $T>0$ fixed. We consider the optimal control problem for analytic affine
systems: $\ds{\dot{x}=f\_0(x)+\sum\_{i=1}^m u\_if\_i(x)}$, with a cost of the
form: $\ds{C(u)=\int\_0^T \sum\_{i=1}^m u\_i^2(t)dt}$. For this kind of systems
we prove that if there are no minimizing abnormal extremals then the value
function $S$ is subanalytic. Secondly we prove that if there exists an abnormal
minimizer of corank 1 then the set of end-points of minimizers at cost fixed is
tangent to a given hyperplane. We illustrate this situation in sub-Riemannian
geometry.
