DEVELOPMENT OF INFORMATION SYSTEM TGHEORY VIA POLYNOMIAL MATRIX ALGEBRA : A CONTROL ENGINEERING APPROACH

1) 我们将递归 OR 分解（一种数值稳定的计算方法）应用于多项式矩阵分数，从而为连续时间 MIMO 情况构建了模型参考自适应控制系统的新方案。从条件数的角度来看，这优于传统的递归最小二乘法，因此适合计算机处理。2）我们给出了一种通过基于线性矩阵不等式的数值优化方法进行鲁棒稳定性分析的方法，并推广了现有的用于设计鲁棒/最优控制的多项式方法。此外，我们已将此方法应用于飞行控制问题。事实证明，我们的多项式矩阵方法与美国航空航天学会所谓的特征结构分配法有密切的关系。 3)在信息系统理论方面，我们利用运筹学领域广为人知的排队论，对WDM环网的GMPLS光路配置进行了性能评估。我们还提出了一种简单的信元调度方法，用于减少 ATM-ABR 服务上的应用级抖动。4) 我们发现将多项式矩阵方法扩展到 GF(2) 领域时存在一些困难，这是本研究的最终目标之一。因此，我们正在为此继续努力。

1) We have applied the recursive OR factorization, which is known as a numerically stable computational method, to polynomial matrix fraction, thereby constructing a new scheme for Model Reference Adaptive Control System for the continuous-time MIMO case. This is superior to the conventional recursive least square method from a conditional number point of view, and hence is suitable for computer process.2) We have given a method for robust stability analysis by means of a numerical optimization method based upon Linear Matrix Inequality, and generalized an existing polynomial method for designing robust/optimal control. Furthermore, we have applied this method to a flight control problem. Then it has turned out that our polynomial matrix method has a close relationship to what is called eigenstructure assignment method in the American Institute of Aerospace and Aeronautics.3) Concerning information system theory, we have done performance evaluation of light-path configuration with GMPLS for WDM ring networks by means of queueing theory, which is widely known in the area of operations research. We have also proposed a simple cell scheduling method for application level jitter reduction over ATM-ABR service.4) We have found several difficulties in extending our polynomial matrix method to the GF(2) field, which is one of the final goals of this research. We are thus continuing our effort toward this end.