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Applied Interval Analysis

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

  • Book
  • © 2001

Overview

Authors:
  1. Luc Jaulin

    1. Laboratoire des Signaux et Systèmes, CNRS-SUPÉLEC-Université Paris-Sud, France

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  2. Michel Kieffer

    1. Laboratoire des Signaux et Systèmes, CNRS-SUPÉLEC-Université Paris-Sud, France

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  3. Olivier Didrit

    1. Laboratoire des Signaux et Systèmes, CNRS-SUPÉLEC-Université Paris-Sud, France

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  4. Éric Walter

    1. Laboratoire des Signaux et Systèmes, CNRS-SUPÉLEC-Université Paris-Sud, France

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  • An applied text on a mathematical subject of great importance to control engineers and roboticists and with applications in a wide variety of other disciplines
  • Additional electronic material available to aid in the implementation of ideas from the book

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xvi
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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 3-7

  3. Tools

    1. Front Matter

      Pages 9-9
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    2. Interval Analysis

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 11-43

    3. Subpavings

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 45-63

    4. Contractors

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 65-101

    5. Solvers

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 103-137

  4. Applications

    1. Front Matter

      Pages 139-139
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    2. Estimation

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 141-185

    3. Robust Control

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 187-223

    4. Robotics

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 225-268

  5. Implementation

    1. Front Matter

      Pages 269-269
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    2. Automatic Differentiation

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 271-286

    3. Guaranteed Computation with Floating-point Numbers

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 287-299

    4. Do It Yourself

      • Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter
      Pages 301-351

  6. Back Matter

    Pages 353-379
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Keywords

About this book

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 . . .

Reviews

From the reviews:
"Applied Interval Analysis is the right book at the right time to move computing with intervals into the mainstream of engineering, financial, and scientific computing."
G. William Walster, Interval Technology Engineering Manager, Sun Microsystems and Member of the Editorial Board of Reliable Computing

Authors and Affiliations

  • Laboratoire des Signaux et Systèmes, CNRS-SUPÉLEC-Université Paris-Sud, France

    Luc Jaulin, Michel Kieffer, Olivier Didrit, Éric Walter

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