Technical communique: Injectivity analysis using interval analysis: Application to structural identifiability

  • Authors:

  • Sébastien Lagrange;Nicolas Delanoue;Luc Jaulin

  • Affiliations:

  • Laboratoire Ingénierie des Systèmes Automatisés (LISA), 62 avenue Notre Dame du Lac, 49000 Angers, France;Laboratoire Ingénierie des Systèmes Automatisés (LISA), 62 avenue Notre Dame du Lac, 49000 Angers, France;Laboratoire Développement Technologies Nouvelles (DTN), 2 rue François Verny, 29806 Brest Cedex 09, France

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2008

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Abstract

This paper presents a new numerical algorithm based on interval analysis able to prove that a differentiable function f:A@?R^n-R^n is injective. This algorithm also performs a partition of the domain A in subsets A"i where, for all x@?A"i, the cardinality of f^-^1(f(x)) is constant. In the context of parameter estimation, we show how this algorithm provides an efficient and numerical method to study the structural identifiability of parametric models.