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© 2006

Wave Progagation, Observation and Control in 1-d Flexible Multi-Structures

Book

Part of the Mathématiques et Applications book series (MATHAPPLIC, volume 50)

Table of contents

About this book

Introduction

This volume presents a detailed study of partial differential equations on planar graphs modeling networked flexible mechanical structures. Special emphasis is laid on the understanding of wave propagation phenomena, through the analysis of the problems of observability and controllability from small regions of the graph or its boundary. Some of these results are extended to the heat, beam and Schrödinger equations on planar graphs. Designed as a self-contained introductory course on control and observation of networks, the volume contains also some advanced topics and new techniques which may be of interest for researchers in this area. It also includes a list of open problems and topics for future research.

Keywords

control theory multi-structures partial differential equation partial differential equations on graphs string-network wave equation

Authors and affiliations

  1. 1.Departamento de Matemática AplicadaUniversidad Complutense de MadridMadridSpain
  2. 2.Departamento de Matemáticas Facultad de Ciencias, C-XVUniversidad Autónoma de Madrid CantoblancoMadridSpain

Bibliographic information

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Reviews

From the reviews of the first edition:

"This book deals with propagation, observation and control of the vibrations in a l-d model of a multi-body structure consisting of a finite number of flexible strings distributed along a planar graph. … this book provides a source of information for researchers in the area of control and observation of networks. It also can be used as an introductory textbook for graduate students entering the field." (Claudio Giorgi, Mathematical Reviews, Issue 2006 h)

"The study of mechanical systems consisting of elastic elements is of interest in many situations. … The present book studies the one-dimensional model … . The book is of interest to graduate students and researchers seeking to get an insight into the control theory of elastic systems constituting networks in a rigorous manner. … The book should be quite useful to researchers as a source of recent results and references as well as a self-contained treatment of the subject." (Fiazud Din Zaman, Zentralblatt MATH, Vol. 1083, 2006)