Console Upgrade for 500MHz NMR Spectrometer

这个为期三年的奖项支持美国和法国在应用数学领域的合作研究。调查人员是圣路易斯华盛顿大学的克里斯托弗·i·伯恩斯（Christopher I. Byrnes）、T.J.塔恩（T.J. Tarn）和阿尔贝托·伊西多里（Alberto Isidori），以及巴黎多芬大学的让-皮埃尔·奥宾（Jean-Pierre Aubin）。他们的研究目标是利用和协调代数和微分方程中的各种方法来解决非线性系统的调节和控制问题。他们将研究输出调节，通过反馈和系统跟踪来稳定系统。伯恩斯博士和他在华盛顿大学的团队为这次合作带来了将微分几何应用于非线性控制理论的专业知识。这是由法国小组的非线性系统问题的代数方法补充。该项目将受益于不同方法和理论的综合。控制或影响非线性系统的问题是工业研究人员感兴趣的问题。例如，在航空航天工业中，飞机的飞行控制系统是非线性系统，其中微小的变化可能会影响性能。该方法可应用于飞机起飞和降落过程中风切变的控制问题。这项研究也将促进我们对非线性系统的基本理论和现代控制理论的理解。

This three-year award supports U.S.-France cooperative research in applied mathematics. The investigators are Christopher I. Byrnes, T.J. Tarn and Alberto Isidori of Washington University in St. Louis and Jean-Pierre Aubin of the University of Paris-Dauphine. The objective of their research is to utilize and coordinate diverse methodologies in algebraic and differential equations for resolving problems on the regulation and control of nonlinear systems. They will study output regulation, stabilization of systems by feedback and system tracking. Dr. Byrnes and his group at the University of Washington bring to this collaboration expertise in applying differential geometry to theories of nonlinear control. This is complemented by the French group's algebraic approach to problems in nonlinear systems. The project will benefit from the synthesis of the different methodologies and theories. The problem of controlling or influencing nonlinear systems is of interest to researchers in industry. For example, in the aerospace industry, flight control systems for aircraft are nonlinear systems, where small changes can affect performance. The methodology developed by these researchers could be applied to control problems for wind shear in take-off and landing. This research will also advance our understanding of fundamental theories on nonlinear systems and modern control theory.