Mathematical Sciences: Stochastic Control and Nonlinear Estimation

数学科学：随机控制和非线性估计

• 批准号: 9301048
• 负责人: Wendell Fleming
• 金额: $ 19.21万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301048&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Stochastic; Control; Nonlinear

This project involves several topics in optimal stochastic control and nonlinear estimation. The main topic is risk sensitive optimal control. Risk sensitive optimal control provides a link between stochastic and deterministic (robust control) approaches to modelling disturbances in control systems. Two player, zero-sum differential games arise naturally in the analysis. Risk sensitive control also involves large deviations theory for stochastic processes. The methods to be utilized include viscosity solution techniques for nonlinear partial differential equations. Other classes of stochastic control problems suggested by application in finance theory will be studied. In nonlinear estimation, some problems of partially observed random fields arising in image analysis applications, and hidden Markov models, will be investigated. One of the main issues in mathematical control theory and in control applications is the design of control strategies which are insensitive to unfavorable disturbances which may occur within the control system. For plants which can be modelled as linear control systems, there are several effective strategies for obtaining good system performance in the presence of system perturbations and a clear understanding of the connections between the main methods. However many, if not most, practical control systems, such as those required on high performance aircraft, are only poorly, or not at all, modelled as linear control systems. This project seeks to develop methodologies and their interconnections for robust control of nonlinear stochastic control systems analogous to those for linear stochastic control systems.

该项目涉及最优随机控制和非线性估计的几个主题。主要的主题是风险敏感的最优控制。风险敏感的最优控制提供了随机和确定性(鲁棒控制)方法之间的联系，用于对控制系统中的扰动进行建模。两人、零和微分博弈在分析中自然产生。风险敏感控制还涉及随机过程的大偏差理论。所使用的方法包括非线性偏微分方程组的粘性解技术。我们还将研究在金融理论中应用所提出的其他类型的随机控制问题。在非线性估计中，将研究图像分析应用中出现的部分观测随机场和隐马尔可夫模型的一些问题。数学控制理论和控制应用中的主要问题之一是设计对控制系统中可能发生的不利干扰不敏感的控制策略。对于可以建模为线性控制系统的对象，有几种有效的策略可以在存在系统扰动的情况下获得良好的系统性能，并清楚地了解主要方法之间的联系。然而，许多实用的控制系统(如果不是大多数的话)，如高性能飞机所需的控制系统，只是建模得很差，或者根本没有建模为线性控制系统。该项目致力于开发类似于线性随机控制系统的非线性随机控制系统的鲁棒控制方法及其相互联系。