Boundary Control of PDEs

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.

Spis treści:
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.