Mathematical Sciences: Algebraic Methods in Systems Theory

数学科学：系统论中的代数方法

• 批准号: 9610389
• 负责人: Joachim Rosenthal
• 金额: $ 10.5万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9610389&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Algebraic; Methods; Systems

9610389 Rosenthal This project addresses a number of issues in systems theory and coding theory. The main objectives of the proposal are: 1. A unified algebraic theory for general matrix extension problems which, in special situations, covers results of the pole placement and interpolation literature on one side and results on matrix extensions on the other side. 2. An extension of the Hermann-Martin correspondence well known for one dimensional systems to the situation of multidimensional systems. 3. An optimal control theory for linear systems over finite fields which will result in methods for constructing convolutional codes with large free distance, low complexity and simple decoding schemes. Convolutional codes are used in the data transmission over phone lines, in the area of wireless communication and in the transmission of pictures from deep space. Feedback controllers are implemented in many different devices such as aircraft, robots and chemical processes to mention a few. From a mathematical point of view linear feedback controllers and convolutional encoders are governed by similar set of equations. It is the goal of the proposed research to develop a mathematical theory which will lead to improved design techniques for feedback controllers of various type as well as more efficient convolutional encoders and decoders.

小行星9610389 这个项目解决了系统理论和编码中的一些问题 理论该提案的主要目标是：1。统一代数 一般矩阵扩张问题的理论，在特殊情况下， 一方面涵盖极点配置和插值文献的结果 另一边是矩阵扩展的结果。2.的延伸 一维系统中著名的Hermann-Martin对应 多维系统的情况。3.最优控制理论 对于有限域上的线性系统，这将导致方法， 构造大自由距离、低复杂度的卷积码 和简单的解码方案。 卷积码用于电话线上的数据传输， 在无线通信领域以及在图像传输方面， 深空反馈控制器在许多不同的设备中实现 例如飞行器、机器人和化学过程等。从 数学观点线性反馈控制器和卷积 编码器由类似的方程组控制。这是我们的目标。 提出了一项研究，以发展一种数学理论，这将导致 各种类型反馈控制器的改进设计技术 作为更有效的卷积编码器和解码器。