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

通过本课题的研究，取得了以下两个方面的研究成果：1、大规模并行计算机代数系统的开发利用SIMD并行计算机SM-1-和并行LISP语言TUPLE-，.目前，许多并行计算功能，如行列式、逆矩阵、多元多项式矩阵的Smith形式的计算、Grobner基的计算等都已具体实现。这些并行函数的执行速度大约是顺序函数的100倍。2、n维系统理论在第一年，我们主要从事研究实际稳定性。阐明了内稳定性理论和可稳定输出反馈补偿器的设计方法。第二年，我们研究了n维系统的最优控制理论，特别是最优跟踪问题。从而证明了n维系统的某些优化问题可化为一维优化问题。

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.