Boundary regularity of reachable sets of control systems

The reachable set of a differential inclusion has nonsmooth boundary in general. Now we give sufficient conditions on the compact initial set and the differential inclusion x˙(t)∈f(t,x(t),U(t)) (a.e.) so that this topological boundary has “positive erosion”, i.e. it satisfies a uniform interior sphere condition. The proof is based on the close relation between the semiconcave value function of a suitable Mayer problem and its epigraph with positive erosion.