skip to main content
article

Validated numerical methods for systems and control engineering

Published:01 September 2003Publication History
Skip Abstract Section

Abstract

The aim of this research is to investigate the development of numerical methods for systems and control which have a guarantee on accuracy. An end-product of such research is an algorithm which could be described as "infallible" in the following sense: the user would specify a priori a tolerance as small as desired, and the computer would provide an answer which was guaranteed to be accurate to the specified tolerance. Though this is an established subject within Computer Science [5], as well as a few application areas in science and engineering (see [1, Part III]), the direction appears to be quite new in the control systems area. A characteristic feature of previous work is the application of computer algebra tools and the avoidance of floating-point arithmetic.

References

  1. E. Adams and U. Kulisch, editors. Scientific Computing with Automatic Result Verification, volume 189 of Mathematics in Science and Engineering, London, 1993. Academic Press. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. S. Boyd and V. Balakrishnan. A regularity result for the singular values of a transfer matrix and a quadratically convergent algorithm for computing its L∞-norm. Systems and Control Letters, 15(1):1--7, July 1990. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. M. Green and M. C. Smith. Continuity properties of LQG optimal controllers. Systems and Control Letters, 26(1):33--39, September 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. M. Kanno. Guaranteed Accuracy Computations in Systems and Control. PhD thesis, University of Cambridge, 2003. In preparation.Google ScholarGoogle Scholar
  5. W. Krandick and S. Rump, editors. Journal of Symbolic Computation: Special Issue on Validated Numerical Methods and Computer Algebra, volume 24, number 6. Academic Press, December 1997.Google ScholarGoogle Scholar
  6. A. Neumaier. Interval Methods for Systems of Equations. Cambridge University Press, Cambridge, 1990.Google ScholarGoogle Scholar
  7. G. Vinnicombe. Uncertainty and Feedback - H∞ loop-shaping and the μ-gap metric. Imperial College Press, 2001.Google ScholarGoogle Scholar

Index Terms

  1. Validated numerical methods for systems and control engineering
      Index terms have been assigned to the content through auto-classification.

      Recommendations

      Comments

      Login options

      Check if you have access through your login credentials or your institution to get full access on this article.

      Sign in

      Full Access

      • Published in

        cover image ACM SIGSAM Bulletin
        ACM SIGSAM Bulletin  Volume 37, Issue 3
        September 2003
        39 pages
        ISSN:0163-5824
        DOI:10.1145/990353
        Issue’s Table of Contents

        Copyright © 2003 Copyright is held by the owner/author(s)

        Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

        Publisher

        Association for Computing Machinery

        New York, NY, United States

        Publication History

        • Published: 1 September 2003

        Check for updates

        Qualifiers

        • article
      • Article Metrics

        • Downloads (Last 12 months)0
        • Downloads (Last 6 weeks)0

        Other Metrics

      PDF Format

      View or Download as a PDF file.

      PDF

      eReader

      View online with eReader.

      eReader