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Boundary Control of PDEs

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Boundary Control of PDEs

Boundary Control of PDEs

A Course on Backstepping Designs
Miroslav Krstic, University of California, San Diego
Andrey Smyshlyaev, University of California, San Diego
December 2008
This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
Hardback
9780898716504
AUD$210.00
inc GST
Hardback
    Description

    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

    Product details

    December 2008
    Hardback
    9780898716504
    200 pages
    261 × 180 × 15 mm
    0.6kg
    This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.

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    Contents

    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.
      • Show more
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    Additional Information
    About the authors
      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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