Research on Stochastic Processes and Optimization

随机过程与优化研究

• 批准号: 9704426
• 负责人: Paul Dupuis
• 金额: $ 12.43万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9704426&HistoricalAwards=false
• 关键词: Research; Stochastic; Processes; Optimization

9704426 Dupuis This project covers three topics: (i) theory and applications of the Skorokhod Problem; (ii) large deviations and risk sensitive control and robust control of queueing networks; and (iii) computational methods for deterministic optimal control problems and related first order nonlinear PDE. The solution to the Skorokhod Problem defines what might be considered the input/output map for a number of exact and approximate models in queueing, communication, economics, and other areas. Except in special cases, little is known about the analytical properties of this mapping. This research will build on prior work of the investigator and H. Ishii which takes a geometric approach to obtaining regularity conditions for the Skorokhod Problem. The main thrust of the present work is the development and application of methods based on convex duality. The second part of the project studies large deviations for queueing networks. The main topic here is the formulation and analysis of risk sensitive criteria for the control and regulation of queueing networks. In almost all models for networks there are errors, approximations, and model uncertainty, and one would like to design control schemes that are insensitive to such errors. Using the duality between exponential integrals and the relative entropy function, one can (at least in the context of diffusions) give a precise quantitative characterization of the additional robustness properties that are obtained when a risk sensitive criteria is used. The investigator will formulate and analyze via large deviation techniques such criteria in a queueing context. The final part of the project considers cmmputational methods for deterministic optimal control problems. The main emphasis here is on the development of practical algorithms with good qualitative properties. This will be done for a class of problems with very similar features that arise in large deviation for diffusions, certain problems fr om computer vision, and robust nonlinear control and robust filtering. Modern communication, computer, and queueing systems are very complicated, and in fact too complicated to analyze in complete detail. As systems become more and more heterogeneous (e.g., different data classes, different quality of service requirements, etc.) the control and regulation of these systems becomes more difficult and less intuitive. The first two parts of this project investigate two approaches to dealing with such systems. When analyzing queueing and communication systems one needs (relatively) simple system models which capture the most important aspects of the true system. Linear systems are unable to capture the system behavior caused by hard constraints (non-negativity of queue lengths, limits on buffer sizes, etc.) and discontinuities that occur naturally in well designed routing and service protocols. Part of this research is to look at alternatives to linear systems. The second part focuses on the study of risk sensitive criteria for such systems. Risk sensitive and robust criteria provide alternatives to traditional criteria for the evaluation of system performance, and it is now understood that they are very useful in situations where model uncertainty and robustness against modeling errors are important. Such robustness properties are always important for communication and manufacturing systems. The aim here is to properly formulate and analyze risk-sensitive criteria for random networks, and to quantify the robustness properties when compared to traditional criteria. The last part of the project is devoted to the development of usable and efficient computational methods for deterministic optimal control problems, and in particular to the class of problems that arise in the second part of the proposal.

小行星9704426 本项目包括三个主题：（i）Skorokhod的理论和应用 问题;（ii）大偏差与风险敏感控制和鲁棒控制的研究 网络;以及（iii）确定性最优控制问题的计算方法， 一阶非线性偏微分方程Skorokhod问题的解决方案定义了什么 可以被认为是许多精确和近似模型的输入/输出映射 在 商业、通讯、经济等领域。除了在特殊情况下， 关于这个映射的分析性质。这项研究将建立在以前的基础上。 研究者和H.石井采用几何方法获得 Skorokhod问题的正则性条件。本工作的主旨是 的 凸对偶方法的发展和应用。 的第二部分 该项目研究了网络的大偏差。这里的主要话题是 制定和分析风险敏感标准，以控制和调节风险 网络.在几乎所有的网络模型中，都存在误差、近似和模型错误。 不确定性，并且人们希望设计对这种不敏感的控制方案。 错误.利用指数积分和相对熵函数之间的对偶性， 人们可以（至少在扩散的上下文中）给出 当使用风险敏感标准时获得的附加鲁棒性属性。 研究者将通过大偏差技术制定和分析此类标准， 上下文。该项目的最后一部分考虑了计算方法， 确定性最优控制问题这里的主要重点是发展 具有良好定性性质的实用算法。这将对一类 具有非常相似的特征的问题在扩散的大偏差中出现，某些 计算机视觉问题，鲁棒非线性控制和鲁棒滤波。 现代通信、计算机和通信系统非常复杂， 和 事实上太复杂了，无法完全详细地分析。随着系统变得越来越 异质的（例如，不同的数据类别、不同的服务质量要求等） 这些系统的控制和调节变得更加困难和不那么直观。的 本项目的前两部分研究了处理此类系统的两种方法。 在分析通信系统时，需要（相对）简单 系统 模型捕捉真实系统的最重要方面。线性系统 无法捕获由硬约束（队列的非负性）引起的系统行为 长度、缓冲区大小限制等）以及井中自然出现的不连续性 设计 路由和服务协议。这项研究的一部分是寻找替代线性 系统.第二部分着重研究了这类系统的风险敏感准则。 风险敏感和稳健的标准提供了传统标准的替代方案， 系统性能的评估，现在已经知道，他们是非常有用的， 模型不确定性和对建模误差的鲁棒性很重要的情况。 这种鲁棒性对于通信和制造始终很重要 系统.这里的目的是正确地制定和分析风险敏感的标准， 随机 网络，并量化与传统标准相比的鲁棒性。 该项目的最后一部分是致力于开发可用和高效的 确定性最优控制问题的计算方法，特别是 第二部分提出的问题。