Representation and Control of Infinite Dimensional Systems

1. Front Matter

   Pages i-xxvii

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2. Introduction

   1. Introduction

      Pages 1-10

3. Finite Dimensional Linear Control Dynamical Systems

   1. Front Matter

      Pages 11-11

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   2. Control of Linear Differential Systems

      Pages 13-45

   3. Linear Quadratic Two-Person Zero-Sum Differential Games

      Pages 47-84

4. Representation of Infinite Dimensional Linear Control Dynamical Systems

   1. Front Matter

      Pages 85-85

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   2. Semigroups of Operators and Interpolation

      Pages 87-172

   3. Variational Theory of Parabolic Systems

      Pages 173-200

   4. Semigroup Methods for Systems With Unbounded Control and Observation Operators

      Pages 201-227

   5. State Space Theory of Differential Systems With Delays

      Pages 229-310

5. Qualitative Properties of Infinite Dimensional Linear Control Dynamical Systems

   1. Front Matter

      Pages 311-311

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   2. Controllability and Observability for a Class of Infinite Dimensional Systems

      Pages 313-382

6. Quadratic Optimal Control: Finite Time Horizon

   1. Front Matter

      Pages 383-383

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   2. Bounded Control Operators: Control Inside the Domain

      Pages 385-429

   3. Unbounded Control Operators: Parabolic Equations With Control on the Boundary

      Pages 431-457

   4. Unbounded Control Operators: Hyperbolic Equations With Control on the Boundary

      Pages 459-475

7. Quadratic Optimal Control: Infinite Time Horizon

   1. Front Matter

      Pages 477-477

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   2. Bounded Control Operators: Control Inside the Domain

      Pages 479-516

   3. Unbounded Control Operators: Parabolic Equations With Control on the Boundary

      Pages 517-527

   4. Unbounded Control Operators: Hyperbolic Equations With Control on the Boundary

      Pages 529-536

A new edition in a single volume Over the past decade, more and more sophisticaced mathematical tools and approaches have been incorporated in the ?eld of Control of in?nite dim- sional systems. This was motivated by a whole range of challenging appli- tions arising from new phenomenologicalstudies, technologicaldevelopments, and more stringent design requirements. At the same time, researchers and advanced engineers have been steadily using an impressive amount of very sophisticated mathematics in their analysis, synthesis, and design of systems. Whatwasregardedastooabstract,specialized,ortheoreticalin1990hasnow become a standard part of the toolkit. The decision to produce a second edition of the original 1992–1993 t- volume edition is further motivated by several other factors. Over the years the book has been recognizedas a key referencein the ?eld, and a revised and corrected edition was desirable. Even if some good books on the control of in?nite dimensional linear systems have appeared since then, we felt that the original material has not aged too much and that the breadth of its presen- tion is still attractiveand very competitive. The result is a completely revised and corrected second edition in a single convenient volume with integrated bibliography and index.

• 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

"I found myself browsing almost every time I looked in the book to work on the review, distracted by some exposition of one item or another of fascinating material...What is presented [in the work] is presented well, and I will continue to find the book valuable as a reference. Such a good treatment of this material is extremely welcome. That was indeed the case for the well-received original two-volume version of 1992–1993, and is now again the case for this second edition."   —Thomas I. Seidman, IEEE Control Systems Magazine (Review of the Second Edition)

"The monograph presents a broad review of the existing results in control theory of infinite-dimensional dynamical systems. Theoretical results are illustrated by many examples and additional comments. The monograph contains an extensive list of recent references concerning the theory of abstract linear systems. Finally, it should be pointed out that the monograph is the second edition of a two-volume monograph published by the same authors in 1993. Many results in the one-volume second edition are completely revised and corrected. Moreover, the second edition contains many new research results."   —Zentralblatt MATH (Review of the Second Edition)

"We state at the outset that 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.... The book makes a worthwhile effort to be accessible and relatively self-contained. [It] should prove to be a valuable source for mathematicians who want to learn more about aspects of deterministic control theory as well as theoretical engineers willing to learn the mathematical tools necessary to give precise formulations and solutions to problems arising from applications."  —Mathematical Reviews (Review of Volume I of the First Edition)

"This book will undoubtedly prove [to be] a very valuable text to researchers familiar with finite-dimensional control theory and methods of functional analysis/semigroup theory who are interested in learning more about PDE systems and their control. This task is greatly facilitated by exploiting analogies with finite-dimensional theory and relying for the most part on operator/semigroup methods, thus reducing to a minimum the necessity of PDE background. The book 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 (Review of Volume II of the First Edition)

"This is a book which people in the field have been waiting for since the late seventies.... The difference [in this book] lies in the scope of the classes of systems which are covered, which is much wider than that covered in earlier texts.... This book is a welcome addition to the literature. It presents a unified, up-to-date treatment of the main approaches to the representation of partial and differential delay systems.... The book is recommended both as an advanced graduate text for mathematicians and as a valuable reference guide to the literature."   —Journal of Mathematical Systems, Estimation, and Control (Review of Volume I of the First Edition)

• School of Management, University of Texas at Dallas, Richardson, USA

  Alain Bensoussan

• Scuola Normale Superiore, Palazzo della Carovana, Pisa, Italy

  Giuseppe Prato

• Centre de recherches mathématiques and Département de mathématiques et de statistique, Université de Montréal, Montréal, Canada

  Michel C. Delfour

• Department of Electrical Engineering and Computer Science Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, USA

  Sanjoy K. Mitter

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