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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...
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