Variational Analysis, Optimization of Eigenvalues, and Robust Stability

变分分析、特征值优化和鲁棒稳定性

• 批准号: 0505712
• 负责人: James Burke
• 金额: --
• 依托单位: University of Washington
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-01 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0505712&HistoricalAwards=false
• 关键词: Variational; Analysis; Optimization; Eigenvalues; Robust

The main focus of the proposed research is the analysis and optimization of various measures of robust stability in linear systems that evolve in time, i.e., linear dynamical systems. Here stability generally refers to the ability of a system to return to steady state after receiving an impulse, e.g., the ability of a structure to stop vibrating after an earthquake. The term "robust stability" refers to notions of stability that attempt to balance the transient stability of a system with its asymptotic stability. The asymptotic stability of a linear system has a well-established relationship to the eigenvalues of the underlying system. However, it has long been recognized in linear dynamics that when the associated linear transformation is highly non-normal the eigenvalues give little or no information about the transient behavior of the system. This transient behavior can be quite unacceptable from the perspective of engineering design and control. This has given rise to the modern focus on transient stability, which generally refers to such properties as bounded transient peaks and/or bounded transient growth/decay rates. The PI and his collaborators have already established a rich foundation of techniques, results, and numerical tools for further progress in this research. They propose to continue this work and to provide efficient numerical tools for engineering design and control practitioners.

拟议研究的主要重点是分析和优化在随时间发展的线性系统（即线性动力学系统）中的各种稳健稳定性度量。 在这里，稳定性通常是指系统在收到冲动后返回稳态的能力，例如，结构在地震后停止振动的能力。 “稳定稳定性”一词是指试图在系统的瞬时稳定性与其渐近稳定性平衡的稳定性概念。 线性系统的渐近稳定性与基础系统的特征值建立了良好的关系。 然而，长期以来，在线性动力学中已经认识到，当相关的线性转换高度非正常时，特征值几乎没有或根本没有有关系统瞬态行为的信息。 从工程设计和控制的角度来看，这种瞬态行为是不可接受的。 这引起了现代对瞬态稳定性的关注，通常指有限的瞬态峰和/或有限的瞬态生长/衰减速率等性质。 PI和他的合作者已经为这项研究的进一步进步建立了丰富的技术，结果和数值工具的基础。 他们建议继续这项工作，并为工程设计和控制从业者提供有效的数值工具。