Development of Parallel Computer Algebra System and its Application to nD system Theory

并行计算机代数系统的发展及其在nD系统理论中的应用

• 批准号: 05650391
• 负责人: SAITO Osami
• 金额: $ 1.28万
• 依托单位: Toyohashi University of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1993
• 资助国家: 日本
• 起止时间: 1993 至 1994
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-05650391/
• 关键词: massively parallel; Computer Algebra; Parallel programming; virtual PE; nD system; stabilizability; Optimal Control; Iteratioe learning Control; 数式処理系; PE間通信; 並列プログラム作成; 並列処理; 並列記号処理; n-Dシステム; 学習制御; 並列アルゴリズム

The following two research results are obtained through this project.1, Development of massively parallel computer algebraThe prototype system of massively parallel computer algebra has been developed by using SIMD parallel computer , -SM-1-, and parallel LISP,-TUPLE-, . At present, many parallel functions such as computations of determinant, inverse matrix and Smith form for the matrices which consist of multivariable polynomial, and Grobner bases have been concretely realized. These parallel functions execute about a hundred times as fast as sequential ones.2, n-D system theoryIn the first year, we have engaged mainly in studying the practical-stability. The theories about internal stability and design methods for stabilizablu output feedback compensator, have been clarified. In the second year, we study the optimal control theory for n-D systems specially optimal tracking problem. Consequently some optimal problems for n-d systems are proved to be reduced to 1D optimal problems.

1.大规模并行计算机代数的研制用SIMD并行机-SM-1-和并行LISP语言-tuple--开发了大规模并行计算机代数原型系统。目前，对于由多元多项式组成的矩阵和Grobner基的行列式、逆矩阵和Smith形式的计算等并行功能已经得到了具体的实现。这些并行函数的执行速度大约是顺序函数的一百倍。2.n维系统理论在第一年，我们主要致力于研究实用稳定性。阐明了内稳定理论和可镇定输出反馈补偿器的设计方法。第二年，我们研究了n-D系统的最优控制理论，特别是最优跟踪问题。从而将n-d系统的一些优化问题归结为一维最优问题。

项目成果

L XU,O SAITO and K ABE: "Practical Internal Stability and Practical-Stabilization by State-Space Approach for nD Systems" Trans. of SICE. Vol. 30, No. 12. 1466-1473 (1994)

L XU、O SAITO 和 K ABE：“nD 系统的实际内部稳定性和状态空间方法的实际稳定” Trans。

L XU,O SAITO and K ABE: "Output feedback Stabilizability and Stabilization Algorithms for 2D systems" Multidimensional Systems and Signal Processing. Vol. 5. 41-60 (1994)

L XU、O SAITO 和 K ABE：“2D 系统的输出反馈稳定性和稳定性算法”多维系统和信号处理。

徐 粒,斉藤,阿部: "nDシステムのPractical内部安定と状況空間法によるPractical安定化" 計測自動制御学会論文誌. 30-12. 1466-1473 (1994)

Yu、Saito、Abe：“nD 系统的实际内部稳定性和使用情境空间方法的实际稳定”，仪器与控制工程师学会汇刊 30-12（1994 年）。

斉藤,山内,高橋: "数式処理系の汎用ユーザインターフェイス" 日本応用数理学会論文誌. 4-4. 75-83 (1994)

Saito、Yamauchi、Takahashi：“数学公式处理系统的通用用户界面”，日本应用数学学会汇刊 4-4（1994 年）。

LiXU,Osami SAITO Kenichi ABE: "The Design of Practically-Stable nD Feedback System" Automatica. 30-9. 1389-1397 (1994)

LiXU，Osami SAITO Kenichi ABE：“实用稳定的 nD 反馈系统的设计”Automatica。