About correctness of some problems of control by material point

The questions connected with attainability with respect to the velocity coordinate for mass point under boundary condition on the state in the last time moment are considered. The property of type of a stability (to within the closure) under the weakening of boundary condition is investigated. For this the comparison of the attainability domain with respect to velocity and the natural attraction set is realized. The coincidence of the last set and the closure of the above-mentioned attainability domain is typical.