论文标题
图形上的波方程的形状，速度和确切的可控性
Shape, Velocity, and Exact Controllability for the Wave Equation on a Graph with Cycle
论文作者
论文摘要
精确的可控性在具有循环的图表上被证明。控件可以是在边界和内部顶点应用的控件的混合。证明的方法首先使用动态参数证明形状可控性和速度可控性，从而解决了它们相关的力矩问题。这使人们能够解决与确切可控性相关的力矩问题。在单个控件（边界或内部）的情况下，表明精确的可控性失败。
Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity controllability, thereby solving their associated moment problems. This enables one to solve the moment problem associated to exact controllability. In the case of a single control, either boundary or interior, it is shown that exact controllability fails.
