Taylor approximation for hybrid systems

  • Authors:

  • Ruggero Lanotte;Simone Tini

  • Affiliations:

  • Dipartimento di Scienze della Cultura, Politiche e dell'Informazione, Università dell'Insubria, Via Valleggio 11, I-22100 Como, Italy;Dipartimento di Scienze della Cultura, Politiche e dell'Informazione, Università dell'Insubria, Via Valleggio 11, I-22100 Como, Italy

  • Venue:
  • Information and Computation
  • Year:
  • 2007

Quantified Score

Hi-index 0.00

Visualization

Abstract

We propose a new approximation technique for Hybrid Automata. Given any Hybrid Automaton H, we call Approx(H,k) the Polynomial Hybrid Automaton obtained by approximating each formula @f in H with the formulae @f"k obtained by replacing the functions in @f with their Taylor polynomial of degree k. We prove that Approx(H,k) is an over-approximation of H. We study the conditions ensuring that, given any @e0, some k"0 exists such that, for all kk"0, the ''distance'' between any vector satisfying @f"k and at least one vector satisfying @f is less than @e. We study also conditions ensuring that, given any @e0, some k"0 exists such that, for all kk"0, the ''distance'' between any configuration reached by Approx(H,k) in n steps and at least one configuration reached by H in n steps is less than @e.