Large-Scale and Parallel Matrix Computations in Linear Control

这个跨学科的项目将致力于研究 大规模解决方案的有效数值方法， 几种基本线性代数的并行计算 线性控制设计和分析中出现的问题 系统.将特别注意发展和 计算上可行的算法的实现：反馈 稳定的大型二阶模型;计算 频率响应和H-无穷范数的大型稀疏 矩阵;并行和高性能计算的重要 矩阵方程，如李雅普诺夫，西尔维斯特，和里卡蒂和 特征值分配问题。一些数值分析 问题的调节和稳定性等方面， 算法也将被考虑。使用 矩阵计算中的最新技术，例如 GMRES和QMR算法，秩显示QR因子分解， 条件估计方案，例如SPICE、ICE、ACE等，和 相关软件包（如LAPACK）将 重点介绍 在这个项目中要开发的算法， 他们在矢量超级计算机和大规模 并行架构将允许快速、准确和可靠 解决实际中出现的大规模控制问题 如大型空间结构的设计，控制 电力系统，以及其他问题，否则不能 在合理的时间内处理，如果有的话。拟议研究 因此，将解决一些关键的研究需求， 控制理论中的大规模并行计算领域 在最近的专家组报告《控制的未来方向》中， 理论：数学的观点”。该项目是及时和 使应用数学家和控制理论家都受益， 工程师

This interdisciplinary project will be devoted to the study of effective numerical methods for large-scale solutions and parallel computations of several fundamental linear algebra problems arising in the design and analysis of linear control systems. Specific attention will be paid to the development and implementation of computationally viable algorithms for: feedback stabilization of the large second-order model; computing the frequency response and the H-infinity norm of a large and sparse matrix; and parallel and high performance computing of important matrix equations such as the Lyapunov, Sylvester, and Riccati and the eigenvalue assignment problems. Some numerical analysis aspects such as conditioning of the problems and stability of the algorithms will be considered, as well. The use of state-of-the-art techniques in matrix computations such as the GMRES and QMR algorithms, Rank Revealing QR factorizations, condition estimations schemes such as SPICE, ICE, ACE, etc., and the associated software packages (e.g. LAPACK) will be emphasized. The algorithms to be developed in this project and their implementations on vector supercomputer and massive parallel architectures will permit fast, accurate, and reliable solutions of large-scale control problems arising in practical situations such as the design of large space structures, control of power systems, and for other problems that otherwise could not be handled in a reasonable time, if at all. The proposed research will thus address some of the critical needs for research in the area of large-scale and parallel computations in control theory outlined in the recent panel report "Future Directions in Control Theory: A Mathematical Perspective". The project is timely and benefit both applied mathematicians and control theorists and engineers.