Model Reduction for Structured Dynamical Systems

结构化动力系统的模型简化

• 批准号: 0306503
• 负责人: Danny Sorensen
• 金额: $ 43.66万
• 依托单位: William Marsh Rice University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-08-15 至 2007-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0306503&HistoricalAwards=false
• 关键词: Model; Reduction; Structured; Dynamical; Systems

This project is concerned with the investigation of five specific topics in model reduction. (a) Decay rates of certain system related singular values (Hankel singular values and others related to approximation error bounds); (b) Model reduction for passive systems; (c) Convergence of Krylov-like projection algorithms for model reduction and the establishment of error bounds for such methods; (d) Reduction methods for periodically time-varying systems, and (e) Structure preserving reduction methods for second order dynamical systems.Model reduction seeks to replace a large-scale system of differential or difference equations by a system of substantially lower dimension, that ideally, has the same response characteristics as the original system, yet requires far less computational resources for realization. Such large-scale systems arise in circuit simulation; they also arise through spatial discretization of certain time dependent PDE control systems and in many other applications. For example, an important step in chip manufacturing is the physical verification step, where a detailed simulation, modeling all constituent components of the chip must be carried out to check its behavior. Full simulation is out of the question due to computational complexity. Simulation based upon a reduced model is required to complete the computation in a reasonable period of time. However, it is essential that accuracy of the results is sufficient and that salient physical properties of the chip are faithfully preserved with the reduced model. This research is focused on the development, analysis, and implementation of reduction methods for very large problems. Where needed, the work will involve extending the underlying theory of dimension reduction, particularly for control problems. The primary goal is to provide reliable and efficient dimension reduction methods that preserve structure and system properties with rigorously established bounds on approximation error.

本计画主要探讨模型降阶中的五个特定主题。(a)某些系统相关奇异值的衰减率（B）无源系统的模型降阶;（c）模型降阶的Krylov类投影算法的收敛性和这种方法的误差界的建立;（d）周期性时变系统的归约方法，以及（e）二阶动力系统的结构保持降阶方法。模型降阶寻求用基本上更低维度的系统来替换大规模的微分或差分方程系统，理想地，具有与原始系统相同的响应特性，但需要少得多的计算资源来实现。这样的大规模系统出现在电路仿真中，它们也出现在某些时间相关的PDE控制系统的空间离散化和许多其他应用中。例如，芯片制造中的一个重要步骤是物理验证步骤，其中必须执行详细的仿真，对芯片的所有组成部件进行建模，以检查其行为。由于计算复杂性，完全模拟是不可能的。为了在合理的时间内完成计算，需要在简化模型的基础上进行仿真。然而，重要的是，结果的准确性是足够的，并且芯片的显著物理特性被忠实地保留在简化模型中。这项研究的重点是非常大的问题的减少方法的开发，分析和实施。在需要的地方，工作将涉及扩展基本的降维理论，特别是控制问题。其主要目标是提供可靠和有效的降维方法，保持结构和系统的性质与严格建立的近似误差的界限。