Optimal Linear-Quadratic Controller Design

Abstract

Linear quadratic optimal control is one of the most well-known approaches to controller design. The aim is to response of the system to the initial condition. There is a quadratic cost on the state and also the control. In this chapter, the theory for infinite-dimensional systems is described. As in the rest of this book, only bounded control operators are considered. An important issue is computation of the optimal linear quadratic controller. This is generally done via approximation of a Riccati equation. Standard PDE approximation methods are not always successful when used for controller design. Sufficient conditions for an approximation scheme to yield reliable results are provided. Also, for some problems, particularly those in more than one space dimension, the lumped approximation can be of high order. Standard direct methods can not always be used. A description of several methods for solution of algebraic Riccati equations is provided. Control actuator location can have a dramatic effect on control system performance for DPS. It should be considered part of controller synthesis. Results on this aspect of controller are described and illustrated.