Large-Scale Scientific Computing in Control

这项建议描述了一个跨学科研究项目，其主要目标是扩展控制和系统理论的计算前沿。概述了计算考虑的层次，从小阶数问题到大阶数问题。最近的分析技术将得到改进和推广，这些技术证明了前者的标准算法的数值局限性。然而，主要的研究重点将是高阶问题，对于这些问题，目前几乎没有可靠的数值技术，特别是对于由所谓的二阶矩阵形式的模型引起的问题。这样的模型自然而然地出现在工程和科学的大多数分支中。建议扩展各种控制和系统理论算法，以利用普遍存在的二阶方程中可用的特殊矩阵结构。并行算法和专门的计算体系结构为迎接在线和离线计算的先进控制策略的挑战提供了很有前途的机会。通过研究基本和普遍感兴趣的问题(特别是由二阶模型产生的问题)，该项目将贡献并行算法和软件，以支持从高性能飞机发动机的主动控制到大型空间结构的振动控制到互联电力系统控制等问题中产生的计算。这样的应用将需要在速度和可解决问题的大小方面至少提高一个数量级。将密切关注基本的数值问题，如条件调节和稳定性；将算法应用到可靠和健壮的软件中，将有助于向工业界、政府和学术界进行有效的技术转让。

This proposal describes an interdisciplinary research project whose principal objective is to extend the computational frontiers of control and system theory. A hierarchy of computational considerations is outlined, ranging from small-order problems to large-order problems. Recent analytic techniques which demonstrate numerical limitations of standard algorithms for the former will be improved and extended. However, the principal research thrust will be towards high-order problems for which rather few dependable numerical techniques presently exist, particularly for problems arising from models in so-called second-order matrix form. Such models arise naturally throughout most branches of engineering and the sciences. It is proposed to extend various control and system theory algorithms to exploit the special matrix structures available in the ubiquitous second-order equations. Parallel algorithms and specialized computing architectures offer promising opportunities to meet the challenge of advanced control strategies for both on-line and off-line computations. By examining problems of fundamental and generic interest (especially those generated by second-order models), this project will contribute parallel algorithms and software to support computations arising in problems ranging from active control for high performance aircraft engines to vibration control for large space structures to control of interconnected power systems. Such applications will require at least an order of magnitude improvement in speed and the size of problems solvable. Close attention will be paid to basic numerical issues such as conditioning and stability; and implementation of algorithms into reliable and robust software will facilitate effective technology transfer to industry, government, and academia.