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Infinite Dimensional Optimization and Control Theory


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: July 2010
  • availability: Available
  • format: Paperback
  • isbn: 9780521154543

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About the Authors
  • This book is on existence and necessary conditions, such as Potryagin's maximum principle, for optimal control problems described by ordinary and partial differential equations. These necessary conditions are obtained from Kuhn–Tucker theorems for nonlinear programming problems in infinite dimensional spaces. The optimal control problems include control constraints, state constraints and target conditions. Evolution partial differential equations are studied using semigroup theory, abstract differential equations in linear spaces, integral equations and interpolation theory. Existence of optimal controls is established for arbitrary control sets by means of a general theory of relaxed controls. Applications include nonlinear systems described by partial differential equations of hyperbolic and parabolic type and results on convergence of suboptimal controls.

    • Unifies finite and infinite dimensional control problems
    • Deals with the important problems of target conditions and state constraints
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    Reviews & endorsements

    Review of the hardback: 'This outstanding monograph will be a great source both for experts and for graduate students interested in calculus of variations, non-linear programming, optimisation theory, optimal control and relaxation theory.' European Mathematical Society

    Review of the hardback: '… an impressive monograph on infinite dimensional optimal control theory. This is an original and extensive contribution which is not covered by other recent books in the control theory.' J. P. Raymond, Zentralblatt für Mathematik

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    Product details

    • Date Published: July 2010
    • format: Paperback
    • isbn: 9780521154543
    • length: 816 pages
    • dimensions: 229 x 152 x 41 mm
    • weight: 1.07kg
    • availability: Available
  • Table of Contents

    Part I. Finite Dimensional Control Problems:
    1. Calculus of variations and control theory
    2. Optimal control problems without target conditions
    3. Abstract minimization problems: the minimum principle for the time optimal problem
    4. Abstract minimization problems: the minimum principle for general optimal control problems
    Part II. Infinite Dimensional Control Problems:
    5. Differential equations in Banach spaces and semigroup theory
    6. Abstract minimization problems in Hilbert spaces: applications to hyperbolic control systems
    7. Abstract minimization problems in Banach spaces: abstract parabolic linear and semilinear equations
    8. Interpolation and domains of fractional powers
    9. Linear control systems
    10. Optimal control problems with state constraints
    11. Optimal control problems with state constraints: The abstract parabolic case
    Part III. Relaxed Controls:
    12. Spaces of relaxed controls: topology and measure theory
    13. Relaxed controls in finite dimensional systems: existence theory
    14. Relaxed controls in infinite dimensional spaces: existence theory.

  • Author

    Hector O. Fattorini, University of California, Los Angeles
    Hector O. Fattorini graduated from the Licenciado en Matemática, Universidad de Buenos Aires in 1960 and gained a Ph.D. in Mathematics from the Courant Institute of Mathematical Sciences, New York University, in 1965. Since 1967, he has been a member of the Department of Mathematics at the University of California, Los Angeles.

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