Boundary Control of PDEs: A Course on Backstepping Designs
Miroslav Krstic and Andrey Smyshlyaev

SIAM, 2008, ISBN 978-0-89871-650-4

CONTENTS:

Chapter 1: Introduction 1

Chapter 2: Lyapunov Stability 13

Chapter 3: Exact Solutions to PDEs 23

Chapter 4: Parabolic PDEs: Reaction-Advection-Diffusion and Other Equations 29

Chapter 5: Observer Design 53

Chapter 6: Complex-Valued PDEs: Schrodinger and Gunzburg-Landau Equations 65

Chapter 7: Hyperbolic PDEs: Wave Equations 79

Chapter 8: Beam Equations 89

Chapter 9: First-Order Hyperbolic PDEs and Delay Equations 109

Chapter 10: Kuramoto-Sivashinsky, Korteweg-de Vries, and Other "Exotic" Equations 115

Chapter 11: Navier-Stokes Equations 119

Chapter 12: Motion Planning for PDEs 131

Chapter 13: Adaptive Control for PDEs 145

Chapter 14: Towards Nonlinear PDEs 161

Appendix: Bessell Functions 173

Bibliography 177

Index 191

From back cover:

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.