ITR/AP: Collaborative Research: Model Reduction of Dynamical Systems for Real Time Control

ITR/AP：协作研究：实时控制动态系统的模型简化

• 批准号: 0324944
• 负责人: Kyle Gallivan
• 金额: $ 41.45万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-01 至 2008-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0324944&HistoricalAwards=false
• 关键词: ITR; AP; Collaborative; Research; Model

This project proposes to extend the methods we have developed for model reduction of large-scale Linear Time Invariant (LTI) systems to a new regime of problems that require adaptive models. In particular, we will consider large-scale structured problems that are either time-varying, or which require adaptive updating of the initial reduced models to obtain better approximation properties.Intellectual MeritThe research proposed here will provide efficient and robust methods for producing reduced order models of large state-space systems. This activity is expected to have an impact on system theory of complex systems, parallel numerical linear algebra for large-scale problems, and on efficient implementation of these schemes on parallel and distributed platforms. Once the theory and computational methods are developed, we expect that high quality software will result and have applications in many areas of engineering. This will enable the design of real time controllers for complex systems. This project will also have an impact on the education of students in computational science and engineering, both at the undergraduate and the graduate levels.Broader ImpactThe proposed project leverages extensively the existing intellectual and equipment infrastructure at Purdue, Rice, and Florida State Universities, as well as the Catholic University of Louvain, Belgium. The overall group of PI's and senior personnel bring extensive expertise and experience in dynamical systems, model reduction, control theory, seismic design and analysis of structures, numerical linear algebra, geometric modeling, data analysis and visualization, and parallel computing. In fact, collectively, they have had experience in designing and implementing numerical linear algebra algorithms on most of the significant high-performance commercial architectures and many of the experimental parallel architectures since the Illiac IV (designed and built in the late 1960's!). The three groups complement one another perfectly and are well-poised to successfully realize the goals of this proposal.

该项目建议将我们开发的大规模线性时不变（LTI）系统模型简化方法扩展到需要自适应模型的新问题领域。特别是，我们将考虑时变的大规模结构化问题，或者需要自适应更新初始降阶模型以获得更好的近似属性。智力优点这里提出的研究将为生成降阶模型提供有效且稳健的方法大型状态空间系统。这项活动预计将对复杂系统的系统理论、大规模问题的并行数值线性代数以及这些方案在并行和分布式平台上的有效实现产生影响。一旦理论和计算方法得到发展，我们预计将产生高质量的软件并在许多工程领域得到应用。这将使复杂系统的实时控制器设计成为可能。该项目还将对本科生和研究生阶段的计算科学和工程学生的教育产生影响。更广泛的影响拟议的项目广泛利用普渡大学、莱斯大学和佛罗里达州立大学现有的知识和设备基础设施，以及比利时鲁汶天主教大学。整个 PI 和高级人员团队在动力系统、模型简化、控制理论、结构抗震设计和分析、数值线性代数、几何建模、数据分析和可视化以及并行计算方面带来了丰富的专业知识和经验。事实上，总的来说，他们在大多数重要的高性能商业架构和自 Illiac IV（1960 年代末设计和构建！）以来的许多实验性并行架构上都有设计和实现数值线性代数算法的经验。这三个小组完美地互补，并准备好成功实现该提案的目标。