论文标题
在将非平滑系统从一个点带到另一个问题的问题中的准变性下降方法
A Method of the Quasidifferential Descent in a Problem of Bringing a Nonsmooth System from One Point to Another
论文作者
论文摘要
本文考虑了构建程序控件的问题，该程序控制的对象由右侧非平滑（但仅是准相互作用）的系统描述。控制的目的是将这样的系统从给定的初始位置带到一定有限的时间到给定的最终状态。可允许的控件是分段连续和有界的矢量功能，并具有一些平行iped的值。最初的问题简化为对某些惩罚功能的无条件最小化，该功能以微分方程的形式考虑了约束，对象的初始位置和最终位置的约束以及对控件的约束。此外，众所周知，这种功能性在原始问题的解决方案上消失了，仅在其解决方案上消失了。证明了该功能的准分性，最低限度的必要条件和足够条件是根据准差异的。此外，为了解决功能空间中获得的最小化问题，应用了准差下降的方法。示例证明了开发的算法。
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.
