Mathematical Sciences: Exact Controllability and Uniform Stabilization for Higher Dimensional Wave and Plate Equations

这项建议是为了支持在Lasiecka、Triggiani和Lagnese教授指导下参与项目的研究生。这个特殊的项目是关于由波型偏微分方程描述的系统的边界控制，它被定义为多维空间中的有界域。研究的问题包括结构扰动下的精确可控性、一致镇定性和渐近稳定性的鲁棒性。上述理论发展的应用在机械和电气系统中是广泛的。一个例子可能是大空间结构中振荡的减少。另一个可能与机器人手臂的控制有关。这项活动将有助于培养能够解决现代工程师所面临的一些挑战的科学家。

This proposal is for the support of graduate students involved in a project under the direction of Professors Lasiecka, Triggiani and Lagnese. The particular project is related to the boundary control of systems described by wave-type partial differential equations defined as a bounded domain in many dimension space. Problems to be investigated include those of exact controllability, uniform stabilization, and robustness of asymptotic stability properties under structural perturbations. Applications of the theoretical developments mentioned above are widespread in mechanical and electrical systems. One example might be the reduction in oscillations in large space structures. Another might be related to the control of robot arms. This activity will contribute to the training of scientists who can address some of the challenges facing modern engineers.