- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
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 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.
Contents
List of Figures
List of Tables
Preface
Introduction
Lyapunov Stability
Exact Solutions to PDEs
Parabolic PDEs: Reaction-Advection-Diffusion and Other Equations
Observer Design
Complex-Valued PDEs: Schrodinger and Ginzburg-Landau Equations
Hyperbolic PDEs: Wave Equations
Beam Equations
First-Order Hyperbolic PDEs and Delay Equations
Kuramoto-Sivashinsky, Korteweg-de Vries, and Other "Exotic" Equations
Navier-Stokes Equations
Motion Planning for PDEs
Adaptive Control for PDEs
Towards Nonlinear PDEs
Appendix: Bessel Functions
Bibliography
Index
