A Reduced Basis Approach to the Design of Distributed Parameter Controllers

9622842国王这个项目的重点是减少基础的方法来控制器设计的偏微分方程（PDE）描述的分布参数系统的发展。 第一步的框架涉及使用分布参数控制理论的PDE控制问题，以获得一个显式的无穷维控制律。 该控制器是基于补偿器的设计，使状态估计使用（只需要少量的状态测量），而不是全状态反馈，其中的全部分布状态必须是已知的。 下一步依赖于获得反馈控制算子的反馈函数增益的积分表示。 这些功能增益的特殊空间结构的使用允许近似方案，从而导致低阶控制器。 此外，这种近似激发的局部动态分析将深入了解传感器的布局和设计。 这项工作提供了一个框架，实际控制器的设计是计算效率。 此外，它提供了关于传感器设计的问题的答案，特别是关于移动流体中传感器的类型和位置。 本项目将开发一个实用的框架，用于控制复杂系统，传统方法要么范围有限，要么不切实际。 这个框架提供了一个计算快速和有效的控制设计的基础上的基本数学概念。 这项研究的主要应用之一是通过更好地了解飞机与周围流体的相互作用，设计和放置用于控制高性能飞机的控制装置。 ***

9622842 King This focus of this project is the development of a reduced basis approach to controller design for distributed parameter systems described by partial differential equations (PDEs). The first step in the framework involves using distributed parameter control theory for PDE control problems to obtain an explicit infinite dimensional control law. The controller is based on compensator design so that state estimates are used (requiring only a small number of state measurements) as opposed to full-state feedback, in which the full distributed state must be known. The next step relies on obtaining integral representations of feedback control operators in terms of feedback functional gains. The use of the special spatial structure of these functional gains allows for approximation schemes which result in low-order controllers. Moreover, analysis of local dynamics motivated by such approximations will give insight into sensor placement and design. This work provides a framework for practical controller designs which are computationally efficient. Moreover, it provides answers to questions regarding sensor design, specifically regarding types and locations of sensors within a moving fluid. %%% This project will development a practical framework for the control of complicated systems for which traditional approaches either are limited in scope or are impractical. This framework provides a computationally quick and efficient control design based on fundamental mathematical concepts. One of the principal applications of this research will be to the design and placement of control devices for the control of high performance aircraft, through a better understanding of the interactions of the aircraft with the surrounding fluid. ***