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Boundary Control of PDEs: A Course on Backstepping Designs

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by Miroslav Krstic and Andrey Smyshlyaev


2008 / x + 192 pages / Hardcover / ISBN: 978-0898716-50-4 / List Price $97.50 / SIAM Member Price $68.25 / Order Code DC16

Keywords: control theory, partial differential equations, boundary control, adaptive control, nonlinear control


This concise and highly usable 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; PDEs with third and fourth derivatives in space (including variants of linearized Ginzburg–Landau, Schrodinger, Kuramoto–Sivashinsky, KdV, beam, and Navier–Stokes equations); real-valued as well as complex-valued PDEs; stabilization as well as motion planning and trajectory tracking for PDEs; and elements of adaptive control for PDEs and control of nonlinear PDEs.

Boundary Control of PDEs: A Course on Backstepping Designs is appropriate for courses in control theory and includes homework exercises and a solutions manual that is available from the authors upon request. The results are explicit and the style is accessible; students are not expected to have a background beyond that of a typical engineering or physics graduate. Even an instructor who is not an expert on control of PDEs will find it possible to teach effectively from this book. At the same time, an expert researcher in PDEs looking for novel technical challenges will find many topics of interest, particularly in control synthesis for unstable PDEs, nonlinear PDEs, and PDEs with unknown coefficients.

This book is intended for both beginning and advanced graduate students in a one-quarter or one-semester course on backstepping techniques for boundary control of PDEs. It is also accessible to engineers with no prior training in PDEs.

About the Authors
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. He is coauthor of the classic book Nonlinear and Adaptive Control Design (Wiley, 1995) and of five other research monographs on stochastic nonlinear control, extremum seeking, and control of  Navier–Stokes PDEs. He is a Fellow of the IEEE and a recipient of several awards and best paper prizes.

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.

ISBN: 9780898716504

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