Reachability Analysis of Polynomial Systems Using Linear Programming Relaxations

  • Mohamed Amin Ben Sassi
  • Romain Testylier
  • Thao Dang
  • Antoine Girard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7561)

Abstract

In this paper we propose a new method for reachability analysis of the class of discrete-time polynomial dynamical systems. Our work is based on the approach combining the use of template polyhedra and optimization [25, 7]. These problems are non-convex and are therefore generally difficult to solve exactly. Using the Bernstein form of polynomials, we define a set of equivalent problems which can be relaxed to linear programs. Unlike using affine lower-bound functions in [7], in this work we use piecewise affine lower-bound functions, which allows us to obtain more accurate approximations. In addition, we show that these bounds can be improved by increasing artificially the degree of the polynomials. This new method allows us to compute more accurately guaranteed over-approximations of the reachable sets of discrete-time polynomial dynamical systems. We also show different ways to choose suitable polyhedral templates. Finally, we show the merits of our approach on several examples.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mohamed Amin Ben Sassi
    • 2
  • Romain Testylier
    • 1
  • Thao Dang
    • 1
  • Antoine Girard
    • 2
  1. 1.VerimagUniversité de GrenobleFrance
  2. 2.Laboratoire Jean KuntzmannUniversité de GrenobleFrance

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