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Look Inside Control Theory for Partial Differential Equations

Control Theory for Partial Differential Equations
Continuous and Approximation Theories

Volume 2. Abstract Hyperbolic-like Systems over a Finite Time Horizon


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: April 2011
  • availability: Available
  • format: Paperback
  • isbn: 9780521155687

£ 70.99

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About the Authors
  • Originally published in 2000, this is the second volume of a comprehensive two-volume treatment of quadratic optimal control theory for partial differential equations over a finite or infinite time horizon, and related differential (integral) and algebraic Riccati equations. Both continuous theory and numerical approximation theory are included. The authors use an abstract space, operator theoretic approach, which is based on semigroups methods, and which unifies across a few basic classes of evolution. The various abstract frameworks are motivated by, and ultimately directed to, partial differential equations with boundary/point control. Volume 2 is focused on the optimal control problem over a finite time interval for hyperbolic dynamical systems. A few abstract models are considered, each motivated by a particular canonical hyperbolic dynamics. It presents numerous fascinating results. These volumes will appeal to graduate students and researchers in pure and applied mathematics and theoretical engineering with an interest in optimal control problems.

    • In-depth, comprehensive coverage
    • Wealth of illustrative examples
    • Continuous theory and numerical approximation theory
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    Reviews & endorsements

    Review of the hardback: 'This excellent work will be a key reference for all of those who are interested in the quadratic optimal control of hyperbolic partial differential equations (PDEs) and in general in the control of PDEs.' A. Akutowicz, Zentralblatt für Mathematik

    Review of the hardback: 'The reader will find much important information on various aspects of semigroup theory and on the regularity of solutions of hyperbolic equations.' EMS Newsletter

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    Product details

    • Date Published: April 2011
    • format: Paperback
    • isbn: 9780521155687
    • length: 454 pages
    • dimensions: 234 x 156 x 23 mm
    • weight: 0.63kg
    • availability: Available
  • Table of Contents

    1. Categories
    2. Categories and exact sequences
    3. Change of rings
    4. The Morita theory
    5. Limits in categories
    6. Localization
    7. Local-global methods.

  • Authors

    Irena Lasiecka, University of Virginia

    Roberto Triggiani, University of Virginia

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