Mathematical Sciences: Asymptotic Analysis for Some Stochastic Systems

数学科学：某些随机系统的渐近分析

• 批准号: 8814624
• 负责人: Gang George Yin
• 金额: $ 3.09万
• 依托单位: Wayne State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-01-01 至 1991-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8814624&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Asymptotic; Analysis; Some

This project has three distinct parts: (1). A stopping rule for least squares identification is proposed. It is so designed that with any degree of accuracy, the recursive procedure will terminate if the iterates are inside a confidence ellipsoid with high probability. (2). The robustness problem of some stochastic approximation type algorithms will be investigated. The necessary and sufficient condition for convergence is expected to be derived. (3). The problem of open queueing network with parallel observers will be studied. Nearly optimal control and a suitable numerical algorithm are expected to be obtained. These represent areas in which mathematics may be used to solve problems related to the control of mechanical and electrical systems.

该项目有三个不同的部分： （一）. 最小二乘识别的停止规则是 提出了 它的设计使得在任何精确度下， 递归过程将终止，如果迭代 在一个置信度椭圆体内的概率很高。 （二）、 一类随机逼近的鲁棒性问题 类型算法将被研究。 必要和 期望得到收敛的充分条件。 （三）、 带并联的开放式网络问题 观察员将进行研究。 近似最优控制和 期望获得合适数值算法。 这些代表了数学可以用来 解决与机械控制和 电气系统。