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

通过本项目获得以下两项研究成果。1、大规模并行计算机代数的开发利用SIMD并行计算机- sm -1-和并行LISP - tuple -，开发了大规模并行计算机代数的原型系统。目前，对于由多变量多项式和Grobner基组成的矩阵，已经具体实现了行列式计算、逆矩阵计算和Smith形式计算等许多并行函数。这些并行函数的执行速度大约是顺序函数的100倍。2、n-D系统理论在第一年，我们主要从事实际稳定性的研究。阐明了系统内部稳定的理论和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。从而证明了n-d系统的一些最优问题可以简化为一维最优问题。

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.