Mathematical Sciences: Asymptotic Analysis for Some Stochastic Systems

该项目包括三个不同的部分：(1)。提出了一种最小二乘辨识的停止准则。它的设计使得在任何精度下，如果迭代高概率地位于置信度椭球内，则递归过程将终止。(2)。研究了一些随机逼近类算法的稳健性问题。期望得到收敛的充要条件。(3)。研究具有并行观测器的开放排队网络问题。期望得到接近最优的控制和合适的数值算法。这些代表了数学可以用来解决与机械和电气系统控制有关的问题的领域。

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.