Robust Finite-Dimensional LQG (Linear Quadric Gaussian)-Based Controllers for a Class of Distributed Parameter Systems

摘要

This theses considers the problem of robustly stabilizing infinite-dimensional systems using finite-dimensional controllers. The controllers are assumed to be linear quadratic Gaussian (LQG) based controllers. This research uses a direct approach to demonstrate the existence of finite-dimensional LQG-based controllers that stabilize the nominal system. Once existence is proven, the research focuses on ways to analyze the robustness of the controller. Several types of perturbations are considered, including bounded, relatively bounded, additive, and multiplicative. Several approaches to analyzing robustness are developed. Direct analysis using results from functional analysis is accomplished, followed by an approach called the optimal projection equation approach, and then H-infinity techniques are used to develop a sufficient condition for robustness in the presence of multiplicative perturbations of the plant transfer function. A new interpretation of the linear quadratic Gaussian/loop transfer recovery technique (LQG/LTR) is made for the case of reduced order controllers.