A Reduced Basis Approach to the Design of Distributed Parameter Controllers

9622842 King这个项目的重点是为偏微分方程（PDEs）描述的分布式参数系统的控制器设计开发一种减少基的方法。该框架的第一步涉及将分布参数控制理论应用于PDE控制问题，以获得显式的无限维控制律。控制器基于补偿器设计，因此使用状态估计（只需要少量的状态测量），而不是全状态反馈，其中必须知道完整的分布状态。下一步依赖于根据反馈功能增益获得反馈控制算子的积分表示。这些功能增益的特殊空间结构的使用允许近似方案，从而产生低阶控制器。此外，由这种近似驱动的局部动力学分析将为传感器的放置和设计提供见解。这项工作为实际的控制器设计提供了一个计算效率高的框架。此外，它还提供了有关传感器设计的问题的答案，特别是关于传感器在移动流体中的类型和位置。这个项目将为复杂系统的控制开发一个实用的框架，传统方法要么在范围上有限，要么不切实际。该框架提供了一种基于基本数学概念的计算快速有效的控制设计。这项研究的主要应用之一将是通过更好地了解飞机与周围流体的相互作用，来设计和放置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. ***