  The paper considers the problem of constructing a program control for an
object described by a system with nonsmooth (but only quasidifferentiable)
right-hand side. The goal of control is to bring such a system from a given
initial position to a given final state in a certain finite time. The
admissible controls are piecewise continuous and bounded vector-functions with
values from some parallelepiped. The original problem is reduced to an
unconditional minimization of some penalty functional, which takes into account
constraints in the form of differential equations, constraints on the initial
and the final positions of the object, as well as constraints on controls.
Moreover, it is known that this functional vanishes on the solution of the
original problem and only on it. The quasidifferentiability of this functional
is proved, necessary and sufficient conditions for its minimum are written out
in terms of quasidifferential. Further, in order to solve the obtained
minimization problem in the functional space, the method of the
quasidifferential descent is applied. The algorithm developed is demonstrated
by examples.
