Mathematical Sciences: Studies in Stochastic Adaptive Control

数学科学：随机自适应控制研究

• 批准号: 9623439
• 负责人: Tyrone Duncan
• 金额: $ 22.2万
• 依托单位: University of Kansas Center for Research Inc
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623439&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Stochastic; Adaptive

9623439 Duncan A variety of problems of stochastic adaptive control will be investigated in this project. Stochastic adaptive control is the control of an incompletely known stochastic system. Typically to solve an adaptive control problem it is necessary to identify the unknown parameters of the system and simultaneously to construct a control based on an ergodic cost functional. The stochastic systems to be considered include finite dimensional, linear and nonlinear systems and infinite dimensional systems that include both linear and semilinear partial differential equations. The control for the partial differential equations can occur only on the boundary or at discrete points. Some specific systems include stochastic models in the mathematics of finance and in stochastic manufacturing processes. Since self-optimal adaptive controls often cannot be determined or may not exist, the construction of almost optimal adaptive controls will be continued. An important component of this study is the computational investigations in adaptive control which includes the performance of estimation algorithms and adaptive controls. Many important physical systems are controlled. Typically a system is not completely known and often there are perturbations or errors that can be naturally modeled by noise. The control of an unknown system with noise is called stochastic adaptive control. This project will investigate some stochastic adaptive control problems that have applications to some important physical systems. The investigation includes both theoretical and computational aspects.

这个项目将研究随机自适应控制的各种问题。随机自适应控制是对不完全已知随机系统的控制。通常，为了解决自适应控制问题，需要识别系统的未知参数，同时构造基于遍历代价函数的控制。要考虑的随机系统包括有限维，线性和非线性系统和无限维系统，包括线性和半线性偏微分方程。偏微分方程的控制只能发生在边界上或离散点上。一些具体的系统包括金融数学和随机制造过程中的随机模型。由于自最优自适应控制通常无法确定或可能不存在，因此将继续构建几乎最优的自适应控制。本研究的一个重要组成部分是自适应控制的计算研究，包括估计算法和自适应控制的性能。许多重要的物理系统都是受控的。通常情况下，一个系统是不完全已知的，并且经常存在干扰或错误，这些干扰或错误可以通过噪声自然地建模。对带有噪声的未知系统的控制称为随机自适应控制。本课题将研究一些应用于重要物理系统的随机自适应控制问题。研究包括理论和计算两个方面。