Multidimensional Systems Design: Novel Directions

多维系统设计：新方向

• 批准号: 8415599
• 负责人: Nirmal Bose
• 金额: $ 6.29万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1985
• 资助国家: 美国
• 起止时间: 1985-05-15 至 1986-09-25
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8415599&HistoricalAwards=false
• 关键词: Multidimensional; Systems; Design; Novel; Directions

When a model of a one-dimensional (1-D) system is known precisely, many properties of interest, e.g. stability, can be investigated through the analysis of a set of polynomials in one independent variable. A difficulty in such an analysis is that the set of polynomials may be infinite and the question arises of how to reduce the study of this infinite set to the study of a finite set of low order. Furthermore, the coefficients appearing in the set of polynomials are generally not known precisely and only bounds on the coefficients can be given. This brings up the question of the robustness of the properties of interest to parameter variations. For 1-D systems, these two questions have been reasonably well resolved. The goal of this research is to generalize certain results regarding the above questions for 1-D systems to two- or three-dimensional systems. Such systems are important in a number of engineering applications such as optical image processing and robotics. In particular, the two general research tasks are property invariance of n-dimensional polynomials under coefficient perturbations, and polynomial irreducibility and a type of spectral factorization.

当精确地知道一维（1-D）系统的模型时，许多 感兴趣的性质，例如稳定性，可以通过 对一个自变量的一组多项式的分析。 一 在这种分析中的困难在于多项式的集合可以是 无限的，问题是如何减少对这个问题的研究 无限集的研究是有限集的低阶。 此外，委员会认为， 出现在多项式集合中的系数通常不 已知的精确和只有边界上的系数可以给出。 这 提出了感兴趣的属性的鲁棒性问题 参数变化。 对于一维系统，这两个问题 得到了合理的妥善解决。 本研究的目标是 推广了一维情形下上述问题的某些结果 二维或三维系统。 这种系统 在许多工程应用中是重要 加工和机器人技术。 特别是两个一般性研究任务 是系数下n维多项式的性质不变性 扰动，多项式不可约和一类谱 分解