Calculation formulas for nonsmooth singularities of the optimal result function in a time-optimal problem

Analytical formulas are obtained for extremal points of a singular set in a class of time-optimal problems on a plane. It is proved that the formation of singularities depends directly on the geometry of the target set and on the differential properties of its boundary. Three typical cases are studied and conditions for the appearance of nonsmooth singularities are found. Examples are given.