Estimates for attainability sets of control systems

We consider an approach to the estimation of attainability sets of a control system for solving various control problems. The approach is based on two types of extension of the system, by weakening the finite constraints describing the set of velocities and by diminishing the order of the differential constraint. By combining extensions of both types, one can obtain a sufficiently wide class of estimates from which one can then choose the most effective estimates from the viewpoint of accuracy or simplicity.