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Exact control of genetic networks in a qualitative framework: the bistable switch example

Madalena Chaves 1, * Jean-Luc Gouzé 1 
* Corresponding author
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 : A qualitative method to control piecewise affine differential systems is proposed and explored for application to genetic regulatory networks. This study considers systems whose outputs and inputs are of a qualitative form, well suited to experimental devices: the measurements indicate whether the variables are "strongly" or "weakly" expressed, that is, only the region of the state space where trajectories evolve at each instant can be known. The control laws are piecewise constant functions in each region and in time, and are only allowed to take three qualitative values corresponding to no control (u=1u=1), high synthesis rates (View the MathML sourceu=umax) or low synthesis rates (View the MathML sourceu=umin). The problems of controlling the bistable switch to each of its steady states is considered. Exact solutions are given to asymptotically control the system to either of its two stable steady states. Two approximate solutions are suggested to the problem of controlling the system to the unstable steady state: either control to a neighborhood of the state, or in the form of a periodic cycle that passes through the state.
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Madalena Chaves, Jean-Luc Gouzé. Exact control of genetic networks in a qualitative framework: the bistable switch example. Automatica, Elsevier, 2011, 47 (6), pp.1105-1112. ⟨10.1016/j.automatica.2011.01.071⟩. ⟨hal-00848406⟩

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