论文标题
最佳控制问题的局部最低原理，并具有非规范的混合约束
Local Minimum Principle for an Optimal Control Problem with a Nonregular Mixed Constraint
论文作者
论文摘要
我们考虑了一个不规则的混合不平等约束，即对控件中的梯度在零表面上消失时，最简单的最佳控制问题。 Using the Dubovitskii--Milyutin theorem on the approximate separation of convex cones, we prove a first or der necessary condition for a weak minimum in the form of the so-called local minimum principle, which is formulated in terms of functions of bounded variation, integrable functions, and Lebesgue--Stieltjes measures, and does not use functionals on the space of measurable bounded functions.给出了两个说明性的例子。这项工作基于米卢丁的结果。
We consider the simplest optimal control problem with one nonregular mixed inequality constraint, i.e. when its gradient in the control can vanish on the zero surface. Using the Dubovitskii--Milyutin theorem on the approximate separation of convex cones, we prove a first or der necessary condition for a weak minimum in the form of the so-called local minimum principle, which is formulated in terms of functions of bounded variation, integrable functions, and Lebesgue--Stieltjes measures, and does not use functionals on the space of measurable bounded functions. Two illustrative examples are given. The work is based on results by Milyutin.
