Boundary Control of PDE's

by Krstic, Miroslav; Smyshlyaev, Andrey

• ISBN13: 9780898716504
• ISBN10: 0898716500
• Format: Hardcover
• Copyright: 2008-05-30
• Publisher: Society for Industrial & Applied

Summary

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.

Table of 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: Schrödinger 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

Table of Contents provided by Publisher. All Rights Reserved.