Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems

by Sergei A. Avdonin, Sergei A. Ivanov

Overview

In this book, the authors present the newly developed theory of non-harmonic Fourier series and its applications to the control of distributed parameter systems, and they extend the theory to include vector exponential series. The first part of the book presents the modern theory of exponentials, using an operator theory approach. The second extends and upgrades the method of moments—one of the most powerful tools in the flourishing theory of the control of distributed parameter systems. They then go on to discuss the controllability of systems described by parabolic and hyperbolic PDE's for internal, boundary, initial, and pointwise control, and consider typical applications to optimal control problems. Researchers in control theory, operator theory, functional analysis, and partial differential equations will find much to interest them in this treatise.

Product Details

ISBN-13:	9780521144957
Publisher:	Cambridge University Press
Publication date:	06/24/2010
Edition description:	Reissue
Pages:	324
Product dimensions:	5.90(w) x 9.00(h) x 0.90(d)

Table of Contents

1. Elements of Hilbert spaces theory; 2. Families of vector-valued exponentials; 3. Fourier method in operator equations and controllability types; 4. Controllability of systems of parabolic type; 5. Controllability of systems of hyperbolic type; 6. Control of rectangular membrane vibrations; 7. Boundary control of strings system.

Editorial Reviews

"...a useful tool for people entering the field of harmonic analysis and control as well as for graduate students in applied methematics." Irena Lasiecka, Mathematical Reviews

From the Publisher