Presidential Young Investigators Award

点击翻译按钮获取中文摘要

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.