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

A Method of the Quasidifferential Descent in a Problem of Bringing a Nonsmooth System from One Point to Another