Overview

This monograph explores the modeling of conservation and balance laws of one-dimensional hyperbolic systems using partial differential equations.  It presents typical examples of hyperbolic systems for a wide range of physical engineering applications, allowing readers to understand the concepts in whichever setting is most familiar to them.  With these examples, it also illustrates how control boundary conditions may be defined for the most commonly used control devices. The authors begin with the simple case of systems of two linear conservation laws and then consider the stability of systems under more general boundary conditions that may be differential, nonlinear, or switching.  They then extend their discussion to the case of nonlinear conservation laws and demonstrate the use of Lyapunov functions in this type of analysis.  Systems of balance laws are considered next, starting with the linear variety before they move on to more general cases of nonlinear ones.  They go on to show how the problem of boundary stabilization of systems of two balance laws by both full-state and dynamic output feedback in observer-controller form is solved by using a “backstepping” method, in which the gains of the feedback laws are solutions of an associated system of linear hyperbolic PDEs.  The final chapter presents a case study on the control of navigable rivers to emphasize the main technological features that may occur in real live applications of boundary feedback control. Stability and Boundary Stabilization of 1-D Hyperbolic Systems will be of interest to graduate students and researchers in applied mathematics and control engineering.  The wide range of applications it discusses will help it to have as broad an appeal within these groups as possible.

Full Product Details

Author:   Georges Bastin ,  Jean-Michel Coron
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   Softcover reprint of the original 1st ed. 2016
Volume:   88
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   0.498kg
ISBN:  

9783319811857

ISBN 10:   3319811851
Pages:   307
Publication Date:   22 April 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us.

Table of Contents

Hyperbolic Systems of Balance Laws.- Systems of Two Linear Conservation Laws.- Systems of Linear Conservation Laws.- Systems of Nonlinear Conservation Laws.- Systems of Linear Balance Laws.- Quasi-Linear Hyperbolic Systems.- Backstepping Control.- Case Study: Control of Navigable Rivers.- Appendices.- References.- Index.

Reviews

“A remarkable strong point of the whole book is the inclusion of many illustrative and relevant examples altogether making a convincing case for the direct applicability of the analytic Findings to a number of concrete models. In consequence, this graduate level text should be of interest to advanced students and researchers in applied mathematics and various branches of engineering with a focus on control and stabilization.” (Rainer Picard, Mathematical Reviews, May, 2017)

A remarkable strong point of the whole book is the inclusion of many illustrative and relevant examples altogether making a convincing case for the direct applicability of the analytic Findings to a number of concrete models. In consequence, this graduate level text should be of interest to advanced students and researchers in applied mathematics and various branches of engineering with a focus on control and stabilization. (Rainer Picard, Mathematical Reviews, May, 2017)

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions