PYIA: Optimization and Control of Discrete Event Systems

本研究的主要课题是离散事件随机系统的优化与控制。在优化方面，重点是发展随机逼近和随机优化方法。由于优化离散事件系统的主要困难往往与它的组合性质有关，组合优化中的工具（如拟阵和多拟阵理论）将被纳入这类系统的随机优化中。在控制方面，重点将放在点进程的强度控制上（例如，它驱动排队网络的动态）。随机非线性滤波问题也将在点过程驱动系统的设置中讨论。本研究的理论和方法将应用于两个领域：多媒体通信网络和计算机集成制造系统。这是一项总统青年研究者奖，旨在开展离散事件随机系统的优化和控制研究。这些系统模型是在分析和设计许多重要的工程过程中产生的，如多媒体通信网络和计算机集成制造工厂。预计这项研究的结果将产生更好的理解这些模型和更好的方法来控制这些系统。

The main topic of this research is optimization and control of discrete event stochastic systems. On the optimization side, the focus is on developing stochastic approximation and stochastic optimization methods. Since the major difficulty in optimizing a discrete event system often has to do with its combinatorial nature, tools in combinatorial optimization (e.g. matroid and polymatroid theories) will be incorporated into the stochastic optimization of such systems. On the control side, the focus will be on the intensity control of point processes (which drive the dynamics of a queuing network, for instance). Stochastic non-linear filtering problems will also be addressed in the setting of point process driven systems. Applications of the theory and methodologies developed from this research will be in two areas: multi- media communication networks and computer integrated manufacturing systems. This is a Presidential Young Investigator Award to carry out research into optimization and control of discrete event stochastic systems. These systems models arise in analyzing and designing many important engineering precesses such as multi-media communication networks and computer integrated manufacturing plants. It is expected that the results of this research will yield better understanding of these models and better means of controlling such systems.