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Analyzing Reachability of Linear Dynamic Systems with Parametric Uncertainties

  • Matthias AlthoffEmail author
  • Bruce H. Krogh
  • Olaf Stursberg
Chapter
Part of the Mathematical Engineering book series (MATHENGIN, volume 3)

Abstract

As an important approach to analyzing safety of a dynamic system, this paper considers the task of computing overapproximations of reachable sets, i.e. the set of states which is reachable from a given initial set of states. The class of systems under investigation are linear, time-invariant systems with parametric uncertainties and uncertain but bounded input. The possible set of system matrices due to uncertain parameters is represented by matrix zonotopes and interval matrices – computational techniques for both representations are presented. The reachable set is represented by zonotopes, which makes it possible to apply the approach to systems of 100 continuous state variables with computation times of a few minutes. This is demonstrated for randomized examples as well as a transmission line example.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Matthias Althoff
    • 1
    Email author
  • Bruce H. Krogh
    • 1
  • Olaf Stursberg
    • 2
  1. 1.Carnegie Mellon UniversityPittsburghUSA
  2. 2.Control and System Theory (FB16)University of KasselKasselGermany

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