The paper is devoted to the problem of optimal control of an object described by a system with a continuously differentiable right-hand side and a nondifferentiable (but only quasidifferentiable) quality functional. We consider a problem in the form of Mayer with both a free and a fixed right end. Admissible controls are piecewise continuous (with a finite number of discontinuity points) and bounded vector-functions, which belong to certain polyhedron at each moment of time. Standard discretization of the initial system and control parameterization are performed, and theorems on the convergence of the discrete system solution obtained to the desired solution of the continuous problem are presented. Further, for the discrete system obtained, the necessary and, in some cases, sufficient minimum conditions are written in terms of quasidifferential. The quasidifferential descent method is applied to this problem. The algorithm developed is demonstrated by examples.

本文致力于通过具有连续可区分的右侧和不可区分（但仅准可区分）质量功能的系统描述的对象的最佳控制问题。我们以Mayer形式同时考虑自由端和固定右端的问题。允许的控件是分段连续的（具有有限数量的不连续点）和有界的矢量函数，它们在每个时刻都属于某些多面体。进行了初始系统的标准离散化和控制参数化，并给出了关于离散系统解的收敛性与连续问题的期望解的收敛性的定理。此外，对于获得的离散系统，以拟微分形式写出必要的（在某些情况下）足够的最小条件。拟微分下降法适用于此问题。实例演示了开发的算法。