Presidential Young Investigators Award

总统青年研究员奖

• 批准号: 9057420
• 负责人: Andrew Packard
• 金额: $ 27.73万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-10-01 至 1997-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9057420&HistoricalAwards=false
• 关键词: Presidential; Young; Investigators; Award

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.

该奖项是为帕卡德博士提供研究支持， 国家科学基金会的总统青年 研究者奖（PYIA）计划。 的目标 PYIA计划是为全国最大的 优秀青年理工科 教师。 该奖项旨在提高能力， 美国学术机构响应高度需求 学术和工程专业的合格科学和工程人才 工业研究和教学。 帕卡德博士的领域 研究是应用数学，重点是线性 代数和控制 要做的研究可以分为三个主题： 分析、设计和建模。具体而言： (1)线性分式变换的分析 这一动机来自控制系统设计， 通常很自然地将单个组件建模为标称 模型，沿着与线性分数扰动集， 一起被称为“模型对”。 结构奇异 矩阵的值（ssv）是概念性的数学工具 它回答了许多关于矩阵行为的问题 当它以线性分数方式扰动时。 的PI 将使用这些工具来研究线性的最佳合成 系统. 他的主要理论目标是发展一种更 统一的方法，其中包括一维， 多维（例如，图像处理）系统。 的 ssv将是这项研究的起点，因为 系统类型、系统属性（如稳定性和 输入/输出范数），以及这些属性的鲁棒性， 相当于ssv测试。 (2)鲁棒控制设计-他计划研究计算 问题与H ∞设计和最优 对角缩放问题（对角缩放“技巧”H- 无穷大到设计鲁棒闭环系统）。 (3)建模-改进的模型缓解了 设备/模型不匹配。 他计划使用ssv和H- infinity从现有建模中生成模型集 工具，通过测量排除模型对（无效）， 并从测量（识别）中产生模型。 他 计划通过实验验证这些理论模型。