Hölder equivalence of the value function for control-affine systems
We prove the continuity and the Hölder equivalence w.r.t. an Euclidean distance of the value function associated with the L cost of the control-affine system = () + ∑ (), satisfying the strong Hörmander condition. This is done by proving a result in the same spirit as the Ball–Box theorem for driftless (or sub-Riemannian) systems. The techniques used are based on a reduction of the control-affine system to a linear but time-dependent one, for which...