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方法扩展到模型减少大规模线性时间不变（LTI）系统的方法到需要自适应模型的新问题。特别是，我们将考虑大规模的结构化问题，这些问题是随时间变化的，或者需要对初始减少模型的自适应更新以获得更好的近似属性。Intellectual值得此研究，此处提出的研究将为生成降低大型状态空间系统的降序订单模型提供有效且可靠的方法。预计该活动将对复杂系统的系统理论，用于大规模问题的平行数值线性代数以及在并行和分布式平台上有效实施这些方案。一旦开发了理论和计算方法，我们希望高质量的软件将在许多工程领域中产生并应用。这将使复杂系统的实时控制器设计。该项目还将在本科和研究生级别的计算科学和工程学学生的教育中产生影响。BROADERIMPACT THE拟议项目在普渡大学，赖斯和佛罗里达州立大学的现有知识和设备基础设施以及贝尔利吉亚州Louvain天主教大学的现有知识和设备基础设施。 PI和高级人员的整体组为动态系统，模型降低，控制理论，地震设计和结构的分析，数值线性代数，几何建模，数据分析和可视化以及并行计算带来了广泛的专业知识和经验。实际上，他们总体上在大多数重要的高性能商业体系结构以及自Illiac IV（1960年代末设计和建造的！）以来，在大多数重要的高性能商业体系结构以及许多实验平行体系结构上设计和实施数值线性代数算法的经验。这三个小组互相补充，并得到充分的努力，以成功地实现该提议的目标。