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Boundary Control of PDEs

Boundary Control of PDEs
A Course on Backstepping Designs

Part of Advances in Design and Control

  • Date Published: September 2008
  • availability: Available in limited markets only
  • format: Hardback
  • isbn: 9780898716504

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About the Authors
  • This concise and practical textbook presents an introduction to backstepping, an elegant new approach to boundary control of partial differential equations (PDEs). Backstepping provides mathematical tools for constructing coordinate transformations and boundary feedback laws for converting complex and unstable PDE systems into elementary, stable, and physically intuitive 'target PDE systems' that are familiar to engineers and physicists. Readers will be introduced to constructive control synthesis and Lyapunov stability analysis for distributed parameter systems. The text's broad coverage includes parabolic PDEs; hyperbolic PDEs of first and second order; fluid, thermal, and structural systems; delay systems; real-valued as well as complex-valued PDEs; and stabilisation as well as motion planning and trajectory tracking for PDEs. Even an instructor with no expertise in control of PDEs will find it possible to teach effectively from this book, while an expert researcher looking for novel technical challenges will find many topics of interest.

    • Includes homework exercises and a solutions manual, which is available from the authors upon request
    • Accessible to both beginning and advanced graduate students, and to engineers with no prior training in PDEs
    • Assumes no background beyond that of a typical engineering or physics graduate
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    Product details

    • Date Published: September 2008
    • format: Hardback
    • isbn: 9780898716504
    • length: 200 pages
    • dimensions: 261 x 180 x 15 mm
    • weight: 0.6kg
    • availability: Available in limited markets only
  • Table of Contents

    List of figures
    List of tables
    Preface
    1. Introduction
    2. Lyapunov stability
    3. Exact solutions to PDEs
    4. Parabolic PDEs: reaction-advection-diffusion and other equations
    5. Observer design
    6. Complex-valued PDEs: Schrödinger and Ginzburg–Landau equations
    7. Hyperbolic PDEs: wave equations
    8. Beam equations
    9. First-order hyperbolic PDEs and delay equations
    10. Kuramoto–Sivashinsky, Korteweg–de Vries, and other 'exotic' equations
    11. Navier–Stokes equations
    12. Motion planning for PDEs
    13. Adaptive control for PDEs
    14. Towards nonlinear PDEs
    Appendix. Bessel functions
    Bibliography
    Index.

  • Authors

    Miroslav Krstic, University of California, San Diego
    Miroslav Krstic is Sorenson Professor of Mechanical and Aerospace Engineering at the University of California, San Diego (UCSD), and the founding Director of the Center for Control Systems and Dynamics at UCSD.

    Andrey Smyshlyaev, University of California, San Diego
    Andrey Smyshlyaev is a postdoctoral scholar at the University of California, San Diego. His research interests include control of distributed parameter systems, adaptive control, and nonlinear control.

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