Research Initiation Award: Maclaurin Series Analysis of Discrete Even Dynamic Systems

本研究项目的目的是为随机离散事件动态系统(DEDS)的建模、分析和设计提供一种新的方法。所提出的方法是基于获得作为决策参数的函数的绩效度量的Maclaurin级数。我们的目标是(I)建立一大类随机DEDS的Maclaurin系数的有效递推表达式，以及(Ii)研究所获得的Maclaurin级数的理论和实际意义。该项目的结果将是对现有随机DEDS方法的有力补充。特别是，为了分析和设计的目的，我们将开发性能度量的简单封闭形式近似，以及一些随机DEDS建模准则，类似于用于连续变量动态系统建模的经典Bode-Nyquist方法中的准则。

The goal of this research project is to develop a new approach for the modelling, analysis and design of stochastic discrete event dynamic systems (DEDS). The proposed approach is based on obtaining the Maclaurin series of the performance measure as a function of a decision parameter. Our objectives are (i) to develop efficient recursive expressions for the Maclaurin coefficients for a large class of stochastic DEDS and (ii) to investigate the theoretical and practical implications of the obtained Maclaurin series. The results of this project would form a powerful complement to existing methodologies for stochastic DEDS. In particular, we will develop simple closed form approximations of the performance measures for the purpose of analysis and design, as well as some stochastic DEDS modelling guidelines analogous to those in the classical Bode-Nyquist methodology for modelling continous variable dynamic systems.