Discrete Abstraction of Multiaffine Systems

  • Hui Kong
  • Ezio Bartocci
  • Sergiy Bogomolov
  • Radu Grosu
  • Thomas A. Henzinger
  • Yu Jiang
  • Christian Schilling
Conference paper

DOI: 10.1007/978-3-319-47151-8_9

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9957)
Cite this paper as:
Kong H. et al. (2016) Discrete Abstraction of Multiaffine Systems. In: Cinquemani E., Donzé A. (eds) Hybrid Systems Biology. HSB 2016. Lecture Notes in Computer Science, vol 9957. Springer, Cham

Abstract

Many biological systems can be modeled as multiaffine hybrid systems. Due to the nonlinearity of multiaffine systems, it is difficult to verify their properties of interest directly. A common strategy to tackle this problem is to construct and analyze a discrete overapproximation of the original system. However, the conservativeness of a discrete abstraction significantly determines the level of confidence we can have in the properties of the original system. In this paper, in order to reduce the conservativeness of a discrete abstraction, we propose a new method based on a sufficient and necessary decision condition for computing discrete transitions between states in the abstract system. We assume the state space partition of a multiaffine system to be based on a set of multivariate polynomials. Hence, a rectangular partition defined in terms of polynomials of the form \((x_i-c)\) is just a simple case of multivariate polynomial partition, and the new decision condition applies naturally. We analyze and demonstrate the improvement of our method over the existing methods using some examples.

Keywords

Multiaffine system Hybrid system Discrete abstraction State space partition Gröbner basis 

Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  • Hui Kong
    • 1
  • Ezio Bartocci
    • 2
  • Sergiy Bogomolov
    • 1
  • Radu Grosu
    • 2
  • Thomas A. Henzinger
    • 1
  • Yu Jiang
    • 3
  • Christian Schilling
    • 4
  1. 1.Institute of Science and Technology AustriaKlosterneuburgAustria
  2. 2.Vienna University of TechnologyViennaAustria
  3. 3.University of Illinois at Urbana-ChampaignChampaignUSA
  4. 4.University of FreiburgFreiburg im BreisgauGermany

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