© 2001

Nonlinear and Robust Control of PDE Systems

Methods and Applications to Transport-Reaction Processes


Part of the Systems & Control: Foundations & Applications book series (SCFA)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Panagiotis D. Christofides
    Pages 1-10
  3. Panagiotis D. Christofides
    Pages 11-46
  4. Panagiotis D. Christofides
    Pages 47-70
  5. Panagiotis D. Christofides
    Pages 71-97
  6. Panagiotis D. Christofides
    Pages 99-121
  7. Panagiotis D. Christofides
    Pages 153-192
  8. Back Matter
    Pages 193-251

About this book


The interest in control of nonlinear partial differential equation (PDE) sys­ tems has been triggered by the need to achieve tight distributed control of transport-reaction processes that exhibit highly nonlinear behavior and strong spatial variations. Drawing from recent advances in dynamics of PDE systems and nonlinear control theory, control of nonlinear PDEs has evolved into a very active research area of systems and control. This book­ the first of its kind- presents general methods for the synthesis of nonlinear and robust feedback controllers for broad classes of nonlinear PDE sys­ tems and illustrates their applications to transport-reaction processes of industrial interest. Specifically, our attention focuses on quasi-linear hyperbolic and parabolic PDE systems for which the manipulated inputs and measured and controlled outputs are distributed in space and bounded. We use geometric and Lyapunov-based control techniques to synthesize nonlinear and robust controllers that use a finite number of measurement sensors and control actuators to achieve stabilization of the closed-loop system, output track­ ing, and attenuation of the effect of model uncertainty. The controllers are successfully applied to numerous convection-reaction and diffusion-reaction processes, including a rapid thermal chemical vapor deposition reactor and a Czochralski crystal growth process. The book includes comparisons of the proposed nonlinear and robust control methods with other approaches and discussions of practical implementation issues.


Diffusion Sensor Tracking control crystal development feedback model partial differential equation process control robust control sensors simulation system transport

Authors and affiliations

  1. 1.Department of Chemical EngineeringUniversity of CaliforniaLos AngelesUSA

Bibliographic information

  • Book Title Nonlinear and Robust Control of PDE Systems
  • Book Subtitle Methods and Applications to Transport-Reaction Processes
  • Authors Panagiotis D. Christofides
  • Series Title Systems & Control: Foundations & Applications
  • DOI
  • Copyright Information Birkhäuser Boston 2001
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-8176-4156-6
  • Softcover ISBN 978-1-4612-6652-5
  • eBook ISBN 978-1-4612-0185-4
  • Series ISSN 2324-9749
  • Edition Number 1
  • Number of Pages XVII, 251
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Systems Theory, Control
    Engineering, general
    Control, Robotics, Mechatronics
  • Buy this book on publisher's site
Industry Sectors
Finance, Business & Banking


"The concrete aspect of this book is its strength, and it may inspire theoreticians in the control of PDEs so that they realize design methods in the finite-dimensional case have interesting extensions in their area; it may encourage practitioners, giving them confidence in dealing with PDEs. The development is illustrated with applications from the chemical industry throughout the book (reactor, chemical vapor deposition, crystal growth)."   —Zentralblatt Math

"This book deals with nonlinear and robust feedback controllers for hyperbolic and parabolic PDEs with fixed spatial domains and parabolic PDEs with time-dependent spatial domains. It includes applications to transport-reaction processes of industrial interest and also discusses practical implementation issues."   —Monatshefte für Mathematik