Description: We study the application of geometric tools applied to nonlinear control problems. This leads to
a coordinate free description of the qualitative features of many nonlinear control models, such as no
holonomic mechanical systems. We also use topological methods to understand the theoretical features of
certain classes of control systems. Our main tools of investigation are sub-Riemannian geometry, singularity
theory, topological tools (e.g. fiber bundle theory, gauge fields etc.) and the theory of nonlinear dynamical
systems.