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

这个项目提出了扩展的方法，我们已经开发的大规模线性时不变（LTI）系统的模型简化到一个新的制度的问题，需要自适应模型。特别是，我们将考虑大规模的结构化问题，无论是随时间变化的，或需要自适应更新的初始简化模型，以获得更好的approximatelyproperties.Intellectual MeritThe这里提出的研究将提供有效的和强大的方法，用于生产大的状态空间系统的降阶模型。这项活动预计将产生影响的复杂系统的系统理论，并行数值线性代数的大规模问题，并有效地实施这些计划的并行和分布式平台。一旦理论和计算方法被开发出来，我们期望高质量的软件将在工程的许多领域得到应用。这将使复杂系统的真实的时间控制器的设计。该项目也将对计算科学和工程专业的本科生和研究生的教育产生影响。更广泛的影响拟议的项目广泛利用普渡大学、赖斯大学、佛罗里达州立大学以及比利时鲁汶天主教大学现有的知识和设备基础设施。整个PI团队和高级人员在动力系统、模型简化、控制理论、抗震设计和结构分析、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拥有丰富的专业知识和经验。事实上，总的来说，他们已经在大多数重要的高性能商业架构和许多实验并行架构上设计和实现数值线性代数算法的经验，因为Illiac IV（设计和建造于20世纪60年代后期！）。这三个集团相互补充，完全有能力成功实现本提案的目标。

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.