The Robust Hurwitz Design Problem

鲁棒 Hurwitz 设计问题

• 批准号: 8612948
• 负责人: B. Ross Barmish
• 金额: $ 21.43万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1986
• 资助国家: 美国
• 起止时间: 1986-09-15 至 1990-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8612948&HistoricalAwards=false
• 关键词: Robust; Hurwitz; Design; Problem

Recently, considerable attention has been given to problems related to the robust control of systems whose mathematical description includes uncertain parameters. This type of uncertainty arises in a diversity of application areas such as flight control, process control, vehicle control, and network design. Several fundamental issues related to this topic will be explored. The contention here is that many problems of this type (such as stabilization, tracking, compensation against parasitics, etc.) can be reduced to more basic questions about polynomials. To this end, this research first establishes a solid connection between robust control problems and a special class of polynomial problems. The resulting polynomials turn out to have a special structure which will be heavily expoited in the proposed research. The unifying polymial framework readily accommodates changes in order and uncertainties which range over a continuum rather than a finite set. The intention is to develop specific compensator design procedures. Much of the impetus for the development of numerical methods is derived from a recent breakthrough in the theory of interval polynomials by Kharitonov.

近年来，数学描述中包含不确定参数的系统的鲁棒控制问题引起了人们的广泛关注。这种类型的不确定性出现在各种应用领域，如飞行控制、过程控制、飞行器控制和网络设计。与此主题相关的几个基本问题将被探讨。这里的论点是，许多这类问题（如稳定、跟踪、抗寄生补偿等）可以简化为关于多项式的更基本的问题。为此，本研究首先建立了鲁棒控制问题与一类特殊多项式问题之间的牢固联系。所得到的多项式具有特殊的结构，这将在本文的研究中得到大量的展示。统一的多项式框架很容易适应顺序和不确定性的变化，这些变化的范围是连续体而不是有限集。目的是制定具体的补偿器设计程序。数值方法发展的动力很大程度上来源于Kharitonov最近在区间多项式理论方面的突破。