Presidential Young Investigators Award

该奖项是在国家科学基金会总统青年研究者奖（PYIA）计划下为帕卡德博士提供研究支持。PYIA计划的目标是为美国最杰出和最有前途的年轻科学和工程教师提供支持。该奖项旨在提高美国学术机构的能力，以满足学术和工业研究和教学对高素质科学和工程人员的需求。帕卡德博士的研究领域是应用数学，重点是线性代数和控制。所要做的研究可以分为三个主题：分析、设计和建模。具体:(1)线性分数变换的分析——这样做的动机来自控制系统设计，其中通常很自然地将单个组件建模为标称模型，以及线性分数摄动集，他们一起被称为“模范对”。矩阵的结构奇异值（ssv）是一个概念性的数学工具，它回答了关于矩阵在线性分式扰动下的行为的许多问题。PI将使用这些工具来研究线性系统的最佳综合。他的主要理论目标是开发一种更统一的方法，包括一维和多维（例如，图像处理）系统。ssv将是本研究的起点，因为这两种类型的系统、系统属性（如稳定性和输入/输出规范）以及这些属性的鲁棒性都相当于ssv测试。(2)鲁棒控制设计-他计划研究H-∞设计的计算问题和最优对角缩放问题（对角缩放“欺骗”H-∞设计鲁棒闭环系统）。(3)建模-改进的模型缓解了植物/模型不匹配的问题。他计划使用ssv和H- infinity从现有的建模工具中生成模型集，通过测量排除模型对（无效），并从测量中生成模型（识别）。他计划用实验来验证这些理论模型。

This award is to provide research support to Dr. Packard under the National Science Foundation's Presidential Young Investigator Awards (PYIA) Program. The objectives of the PYIA Program are to provide support to the Nation's most outstanding and promising young science and engineering faculty. The awards are intended to improve the capability of U.S. academic institutions to respond to the demand for highly qualified science and engineering personnel for academic and industrial research and teaching. Dr. Packard's field of research is applied mathematics, with emphasis on linear algebra and control. The research to be done can be split into three topics: analysis, design and modeling. Specifically: (1) Analysis of linear fractional transformations- The motivation for this comes from control system design where it is often natural to model individual components as a nominal model, along with a linear fractional perturbation set, which together are called the "model pair". The structured singular value (ssv) of a matrix is the conceptual mathematical tool which answers many questions about the behavior of the matrix when it is perturbed in a linear fractional manner. The PI will use these tools to study the optimal synthesis of linear systems. His main theoretical goal is to develop a more unified approach which includes both one-dimensional, and multidimensional (for example, image processing) systems. The ssv will be the starting point for this research, since both types of systems, system properties (such as stability and input/output norms), and the robustness of these properties, are equivalent to ssv tests. (2) Robust Control Design- He plans to study computational problems with H-infinity design and the optimal diagonally scaled problem (the diagonal scaling "tricks" H- infinity into designing robust closed loop systems). (3) Modeling- Improved models alleviate the problems of plant/model mismatch. He plans to use ssv and H- infinity to produce sets of models from existing modeling tools, rule out model pairs via measurements (invalidation), and produce models from measurements (identification). He plans to experimentally verify these theoretical models.