论文标题
封闭字符串II的渐近控制理论
Asymptotic control theory for a closed string II
论文作者
论文摘要
我们为最简单的分布式（无限尺寸）振荡系统之一开发了一个渐近控制理论，即，在应用于单个区分点的有界负载下的封闭串。我们发现精确的字符串状态，这些琴弦状态允许完整的阻尼和所需时间的渐近确切值。通过使用近似可及的集合而不是确切的集合，我们设计了一个反馈控制，事实证明这是渐近的最佳选择。主要结果是可涉及的集合的渐近形状，渐近最佳运动时间以及因此构建的渐近最佳控制的确切代数公式。
We develop an asymptotical control theory for one of the simplest distributed (infinite dimensional) oscillating systems, namely, for a closed string under a bounded load applied to a single distinguished point. We find exact classes of string states that admit complete damping and an asymptotically exact value of the required time. By using approximate reachable sets instead of exact ones, we design a feedback control, which turns out to be asymptotically optimal. The main results are an exact algebraic formula for asymptotic shape of the reachable sets, asymptotically optimal time of motion, and an asymptotically optimal control thus constructed.
