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Collaborative Research: Ergodic Control of Stochastic Differential Equations Driven By a Class of Pure-Jump Levy Processes, and Applications to Stochastic Networks

合作研究：一类纯跳跃 Levy 过程驱动的随机微分方程的遍历控制及其在随机网络中的应用

基本信息

批准号：
1715875
负责人：
Guodong Pang
金额：
$ 21.17万
依托单位：
Pennsylvania State Univ University Park
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-06-01 至 2022-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1715875&HistoricalAwards=false
关键词：
Collaborative Research Ergodic Control Stochastic

项目摘要

Queueing processes in large-scale networks are ubiquitous in society as exemplified by patient flow in hospitals, telephone call centers, service networks, and manufacturing and service operations management. This research will provide fundamental theoretical understanding of these queueing processes in the presence of batch arrivals. The results of this research will be put into direct applications to real-world stochastic networks through collaborations with the health systems and system analysis industry. This research will support under-represented minority groups and train young STEM graduates with new mathematical skills. This research concerns ergodic control problems for systems described by Ito stochastic differential equations (SDEs) driven by pure-jump Levy processes. The research objectives are: (1) to develop a comprehensive theoretical framework for ergodic control for a large class of controlled SDEs driven by a pure-jump Levy process; (2) to study a novel fully nonlinear problem that arises in admission control and falls outside the usual paradigm of stochastic control; and (3) to develop value iteration algorithms and spatial approximation methods in order to study large time asymptotics, and also to facilitate the numerical solution of the associated Hamilton-Jacobi-Bellman (HJB) equations, and the design of learning schemes for adaptive control in the presence of unknown parameters. This research will advance the basic science of applied mathematics and stochastic control, and make fundamental contributions to applied probability and stochastic networks.

大规模网络中的呼叫流程在社会中无处不在，例如医院中的患者流、电话呼叫中心、服务网络以及制造和服务运营管理。这项研究将提供基本的理论理解，在存在批量到达的这些嵌入过程。这项研究的结果将通过与卫生系统和系统分析行业的合作，直接应用于现实世界的随机网络。这项研究将支持代表性不足的少数群体，并培养年轻的STEM毕业生新的数学技能。研究了由纯跳Levy过程驱动的伊藤随机微分方程描述的系统的遍历控制问题。研究目标是：（1）为一类由纯跳Levy过程驱动的受控随机微分方程的遍历控制建立了一个全面的理论框架：（2）研究了一个新的完全非线性问题，该问题出现在接纳控制中，并且福尔斯通常的随机控制范式;（3）发展数值迭代算法和空间逼近方法，研究大时间渐近性，同时也方便了相关Hamilton-Jacobi-Bellman（HJB）方程的数值解，以及在参数未知的情况下自适应控制的学习方案的设计。这一研究将促进应用数学和随机控制的基础科学，并为应用概率和随机网络做出基础性贡献。