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

该项目建议将我们开发的用于大规模线性时不变（LTI）系统模型简化的方法扩展到需要自适应模型的新问题体系。特别是，我们将考虑大规模的结构化问题，这些问题要么是时变的，要么需要自适应更新初始简化模型以获得更好的近似性质。本文提出的研究将为生成大型状态空间系统的降阶模型提供有效和稳健的方法。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施产生影响。一旦理论和计算方法得到发展，我们期望高质量的软件将产生并在许多工程领域得到应用。这将使设计复杂系统的实时控制器成为可能。这个项目也将对本科生和研究生的计算科学和工程专业的教育产生影响。更广泛的影响拟议的项目广泛地利用了普渡大学、莱斯大学、佛罗里达州立大学以及比利时鲁汶天主教大学现有的智力和设备基础设施。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具有丰富的专业知识和经验。事实上，从Illiac IV（设计和建造于20世纪60年代末！）开始，他们就在大多数重要的高性能商业架构和许多实验性并行架构上设计和实现数值线性代数算法。这三个小组相互补充，很好地准备好成功地实现本提案的目标。

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.