Taylor approximation for hybrid systems

  • Authors:

  • Ruggero Lanotte;Simone Tini

  • Affiliations:

  • Dipartimento di Scienze della Cultura, Politiche e dell'Informazione, Università dell'Insubria, Como, Italy;Dipartimento di Scienze della Cultura, Politiche e dell'Informazione, Università dell'Insubria, Como, Italy

  • Venue:
  • HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
  • Year:
  • 2005

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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 φ in H with the formulae φk obtained by replacing the functions in φ 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 ε 0, some k0 exists such that, for all kk0, the “distance” between any vector satisfying φk and at least one vector satisfying φ is less than ε. We study also conditions ensuring that, given any ε 0, some k0 exists such that, for all k k0, 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 ε.