Representation and Control of Infinite Dimensional Systems

  • Alain Bensoussan
  • Giuseppe Da Prato
  • Michel C. Delfour
  • Sanjoy K. Mitter

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

Table of contents

  1. Front Matter
    Pages i-xxvii
  2. Introduction

    1. Pages 1-10
  3. Finite Dimensional Linear Control Dynamical Systems

  4. Representation of Infinite Dimensional Linear Control Dynamical Systems

  5. Qualitative Properties of Infinite Dimensional Linear Control Dynamical Systems

  6. Quadratic Optimal Control: Finite Time Horizon

  7. Quadratic Optimal Control: Infinite Time Horizon

  8. Back Matter
    Pages 537-575

About this book


"This book is a most welcome addition to the literature of this field, where it serves the need for a modern treatment on topics that only very recently have found a satisfactory solution.... Many readers will appreciate the concise exposition."

"Presents, or refers to, the most recent and updated results in the field. For this reason, it should serve as an excellent asset to anyone pursuing a research career in the field."

—Mathematical Reviews (reviews of Volumes I and II of the First Edition)

The quadratic cost optimal control problem for systems described by linear ordinary differential equations occupies a central role in the study of control systems both from a theoretical and design point of view. The study of this problem over an infinite time horizon shows the beautiful interplay between optimality and the qualitative properties of systems such as controllability, observability, stabilizability, and detectability. This theory is far more difficult for infinite dimensional systems such as those with time delays and distributed parameter systems.

This reorganized, revised, and expanded edition of a two-volume set is a self-contained account of quadratic cost optimal control for a large class of infinite dimensional systems. The book is structured into five parts. Part I reviews basic optimal control and game theory of finite dimensional systems, which serves as an introduction to the book. Part II deals with time evolution of some generic controlled infinite dimensional systems and contains a fairly complete account of semigroup theory. It incorporates interpolation theory and exhibits the role of semigroup theory in delay differential and partial differential equations. Part III studies the generic qualitative properties of controlled systems. Parts IV and V examine the optimal control of systems when performance is measured via a quadratic cost. Boundary control of parabolic and hyperbolic systems and exact controllability are also covered.

New material and original features of the Second Edition:

* Part I on finite dimensional controlled dynamical systems contains new material: an expanded chapter on the control of linear systems including a glimpse into H-infinity theory and dissipative systems, and a new chapter on linear quadratic two-person zero-sum differential games.

* A unique chapter on semigroup theory and interpolation of linear operators brings together advanced concepts and techniques that are usually treated independently.

* The material on delay systems and structural operators is not available elsewhere in book form.

Control of infinite dimensional systems has a wide range and growing number of challenging applications. This book is a key reference for anyone working on these applications, which arise from new phenomenological studies, new technological developments, and more stringent design requirements. It will be useful for mathematicians, graduate students, and engineers interested in the field and in the underlying conceptual ideas of systems and control.


H-infinity t Optimal control controllability, observability, stabiliability distributed parameter systems finite dimensional systems game theory hyperbolic equation infinite dimensional systems linear ordinary differential equations linear quadratic differential games max-inf and min-sup problems partial differential equation partial differential equations quadratic optimal control systems with time delays

Authors and affiliations

  • Alain Bensoussan
    • 1
  • Giuseppe Da Prato
    • 2
  • Michel C. Delfour
    • 3
  • Sanjoy K. Mitter
    • 4
  1. 1.School of ManagementUniversity of Texas at DallasRichardsonUSA
  2. 2.Scuola Normale SuperiorePalazzo della CarovanaPisaItaly
  3. 3.Centre de recherches mathématiques and Département de mathématiques et de statistiqueUniversité de MontréalMontréalCanada
  4. 4.Department of Electrical Engineering and Computer Science Laboratory for Information and Decision SystemsMassachusetts Institute of TechnologyCambridgeUSA

Bibliographic information

  • DOI
  • Copyright Information Birkhäuser Boston 2007
  • Publisher Name Birkhäuser Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-4461-1
  • Online ISBN 978-0-8176-4581-6
  • Series Print ISSN 2324-9749
  • Series Online ISSN 2324-9757
  • Buy this book on publisher's site