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

这项建议是为了支持参与Lasiecka、Triggiani和Lagnese教授指导的一个项目的研究生。该项目涉及由定义为多维空间中有界域的波型偏微分方程组描述的系统的边界控制。要研究的问题包括精确可控性、一致镇定和结构摄动下渐近稳定性质的鲁棒性。上述理论发展在机械和电气系统中的应用非常广泛。一个例子可能是大型空间结构中振动的减少。另一个可能与机械臂的控制有关。这项活动将有助于培训能够应对现代工程师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.