Información General

• Autores: Alain Bensoussan, Sanjoy K. Mitter, Michel C. Delfour, Giuseppe Prato
• Editores: Boston : Birkhäuser, 2007
• Año de publicación: 2007
• País: Estados Unidos
• Idioma: inglés
• ISBN: 978-0-8176-4461-1, 978-0-8176-4581-6
• Texto completo no disponible (Saber más ...)

Resumen

• 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.

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Índice

• Preface to the Second Edition
  Preface to Volume I of the First Edition
  Preface to Volume II of the First Edition
  List of Figures
  Introduction
  Part I. Finite Dimensional Linear Control of Dynamical Systems
  Control of Linear Finite Dimensional Differential Systems
  Linear Quadratic Two-Person Zero-Sum Differential Games
  Part II. Representation of Infinite Dimensional Linear Control Dynamical Systems
  Semi-groups of Operators and Interpolation
  Variational Theory of Parabolic Systems
  Semi-group Methods for Systems with Unbounded Control and Observation Operators
  Differential Systems with Delays
  Part III. Qualitative Properties of Linear Control Dynamical Systems
  Controllability and Observability for a Class of Infinite Dimensional Systems
  Part IV. Quadratic Optimal Control: Finite Time Horizon
  Systems with Bounded Control Operators: Control Inside the Domain
  Systems with Unbounded Control Operators: Parabolic Equations with Control on the Boundary
  Systems with Unbounded Control Operators: Hyperbolic Equations with Control on the Boundary
  Part V. Quadratic Optimal Control: Infinite Time Horizon
  Systems with Bounded Control Operators: Control Inside the Domain
  Systems with Unbounded Control Operators: Parabolic Equations with Control on the Boundary
  Systems with Unbounded Control Operators: Hyperbolic Equations with Control on the Boundary
  Appendix A. An Isomorphism Result
  References
  Index