Optimization of Jump Stochastic Systems

9500746 Feinberg本文主要研究连续时间跳跃随机系统的优化问题。具体地说，这项研究旨在发展分析随机系统的新方法：(1)研究最优控制策略的结构，(2)开发计算最优策略的算法，以及(3)发展生产/库存和电信系统中最优策略的结构和计算结果。这位研究者提出了一种分析跳跃随机系统的新方法。这项研究工作的潜力在于，它将为分析具有分段常数轨迹的连续时间马尔可夫决策过程和半马尔可夫决策过程提供一个统一的框架。通过使用新的框架和其他一些建模和分析技术，包括有限和无限维线性规划，研究将致力于开发结构结果和有效的算法来解决连续时间问题，包括具有多准则和约束的问题。该项目的结果将为各种自然和人造系统的动态优化提供分析方法和计算工具，这些系统的行为可以用具有分段恒定轨迹的随机过程来描述。关于如何控制马尔可夫系统以外的动态随机系统的知识还处于初级阶段。这项研究将推动更好地理解和控制广义半马尔可夫过程的前沿。需要能够根据实时数据进行调整的随机模型。这项工作为实现这一目标铺平了道路。

9500746 Feinberg This research is focused on the optimization of continuous time jump stochastic systems. In particular, the research is aimed at developing new methods for analyzing stochastic syqtems: (1) study the structure of optimal control strategies, (2) develop algorithms to compute optimal strategies, and (3) develop structural and computational results for optimal strategies in production/inventory and telecommunications systems. The investigator is proposing a new method of analysis for jump stochastic systems. The potential for the research work is that it will provide a unified framework for the analysis of both the Continuous Time Markov Decision Processes with piecewise constant trajectories and Semi-Markov Decision Processes. By using the new framework and some other modeling and analysis techniques, including finite and infinite-dimensional linear programming, the research will pursue to develop structural results and efficient algorithms for the solution of continuous time problems, including problems with multiple criteria and constraints. The results of this project will provide analytical methods and computational tools for dynamic optimization of a wide range of natural and man-made systems whose behavior can be described by stochastic processes with piecewise constant trajectories. Knowledge of how to control dynamic stochastic systems beyond Markovian systems is in its infancy. This research will advance the frontier toward a better understanding and control of generalized Semi-Markov Processes. Stochastic models that can adjust based on real time data are needed. This work paves the way toward the realization of such a goal.