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2D piecewise affine models approximate real continuous dynamics up to invariant sets

Madalena Chaves 1 Jean-Luc Gouzé 1
1 BIOCORE - Biological control of artificial ecosystems
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique
Abstract : Piecewise affine models often provide a good approximation to describe continuous systems, but may involve a high degree of simplification. To compare solutions of the continuous and piecewise affine models, it is important to quantify the differences between solutions in each region of the state space. As an approach, we will use enveloping " bands " to characterize continuous activation or inhibition functions, and then describe the differences between continuous and piecewise affine solutions in terms of the width δ of these bands. As a case study, we will consider the negative feedback loop, a classical motif in two dimensions which results in oscillating behaviour. For this example, it is shown that the two types of models may differ only on a compact invariant set (the interior of a limit cycle), whose diameter is a function of the band width δ.
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Submitted on : Tuesday, December 6, 2016 - 6:51:49 PM
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Madalena Chaves, Jean-Luc Gouzé. 2D piecewise affine models approximate real continuous dynamics up to invariant sets. NOLCOS 2016 - 10th IFAC Symposium on Nonlinear Control Systems, Aug 2016, Monterey, United States. ⟨hal-01410972⟩

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