Mathematical Sciences: Studies in Stochastic Adaptive Control

小邓肯9623439 随机自适应控制的各种问题将在 这个项目 随机自适应控制是一种不完全自适应控制， 已知随机系统。 通常，为了解决自适应控制问题， 需要识别系统的未知参数， 同时构造基于遍历成本泛函的控制器。 所考虑的随机系统包括有限维、线性、非线性和非线性系统。 非线性系统和无限维系统， 线性和半线性偏微分方程。 的控制器 偏微分方程只能发生在边界上或离散 点 一些特定的系统在数学上包括随机模型 金融和随机制造过程中。 自最优 自适应控制通常不能确定或可能不存在， 将继续构建几乎最佳的自适应控制。 一个 这项研究的一个重要组成部分是计算调查， 自适应控制，包括估计算法的性能 自适应控制。 许多重要的物理系统都受到控制。 通常，系统不 完全已知，并且经常存在可以被 自然地由噪声建模。 带噪声的未知系统的控制 称为随机自适应控制。 该项目将调查一些 随机自适应控制问题，有一些应用 重要的物理系统。 调查包括理论和 计算方面。

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.