Advertisement

Guaranteed Nonlinear Set Estimation via Interval Analysis

  • L. Jaulin
  • É. Walter

Abstract

Many methods have been developed for solving problems arising in mathematics and physics which are formulated in such a way as to require a point solution (e.g., a real number or vector). However, because of the uncertainty attached to the data and numerical errors induced by the finite-word-length representation in the computer, these methods are generally not appropriate to accurately characterize the uncertainty with which the solution is obtained. It is then difficult to assess the validity of the result.

Keywords

Interval Analysis Inclusion Function Principal Plane Vector Interval Natural Interval Extension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Pronzato and E. Walter, Math. Comput. Simul. 32, 571 (1990).MathSciNetCrossRefGoogle Scholar
  2. 2.
    R. E. Moore, Methods and Applications of Interval Analysis, SIAM, Philadelphia, PA (1979).MATHCrossRefGoogle Scholar
  3. 3.
    A. Neumaier, Interval Methods for Systems of Equations, Cambridge University Press, Cambridge, United Kingdom (1990).MATHGoogle Scholar
  4. 4.
    A. Ratschek and J. Rokne, New Computer Methods for Global Optimization, Ellis Horwood Limited, John Wiley & Sons, New York (1988).MATHGoogle Scholar
  5. 5.
    IBM, High-Accuracy Arithmetic Subroutine Library, (ACRITH): Program Description and User’s Guide, SC 33-6164-02, 3rd Ed. (1986).Google Scholar
  6. 6.
    R. Klate, U. W. Kulisch, M. Neaga, D. Ratz, and C. Ullrich, PASCAL-XSC: Language Reference with Examples, Springer-Verlag, Heidelberg, Germany (1992).Google Scholar
  7. 7.
    L. Jaulin and E. Walter, Automatica 29, 1053 (1993).MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    L. Jaulin and E. Walter, Math. Comput. Simul. 35, 123 (1993).MathSciNetCrossRefGoogle Scholar
  9. 9.
    R. E. Moore, Math. Comput. Simul. 34, 113 (1992).CrossRefGoogle Scholar
  10. 10.
    M. Milanese and A. Vicino, Automatica 27, 403 (1991).MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    E. Walter and L. Jaulin, IEEE Trans. Autom. Control 39, 886 (1994).MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • L. Jaulin
    • 1
  • É. Walter
    • 1
  1. 1.Laboratoire des Signaux et SystèmesCNRS École Supérieure d’ElectricitéGif-sur-Yvette CedexFrance

Personalised recommendations