论文标题
波系统的模拟控制
Simulataneous Control of Wave Systems
论文作者
论文摘要
在本文中，我们研究了$ n *的d $ \ d $ \的开放域中波系统的同时可控性。我们获得了由单个控制函数耦合的波方程的共限尺寸空间上的部分可控性结果。我们使用微局部缺陷度量和本征函数的独特延续特性，以证明适当的可观察性不等式适用于空间变化和不同速度与单个控制函数相连的波动方程。对于本征函数的独特延续属性，我们构建了一个反例，以表明在某些指标中，唯一的延续属性不存在。此外，我们研究不同的条件，以确保独特的延续属性。我们还将结果扩展到恒定系数和可能的多个控制功能的情况。在这种情况下，我们证明可控性属性等效于适当的卡尔曼等级条件。
In this paper, we study the simultaneous controllability of wave systems in an open domain of R d , d $\in$ N *. We obtain a partial controllability result on a co-finite dimensional space for wave equations coupled by a single control function. We use microlocal defect measures and the unique continuation property of eigenfunctions to prove that an appropriate observability inequality holds for wave equations with space varying and different speeds coupled by a single control function. For the unique continuation property of eigenfunctions, we construct a counterexample to show that in some metrics, the unique continuation property does not hold. Moreover, we study different conditions to ensure the unique continuation property. We also extend our result to the case of constant coefficients and possibly multiple control functions. In this context, we prove the controllability property is equivalent to an appropriate Kalman rank condition.
