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Control of a Bioreactor with Quantized Measurements

Francis Mairet 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 : We consider the problem of global stabilization of an unstable bioreactor model (e.g. for anaerobic digestion), when the measurements are discrete and in finite number (``quantized''), with control of the dilution rate. The model is a differential system with two variables, and the output is the biomass growth. The measurements define regions in the state space, and they can be perfect or uncertain (i.e. without or with overlaps). We show that a quantized control may lead to global stabilization: trajectories have to follow some transitions between the regions, until the final region where they converge toward the reference equilibrium. On the boundary between regions, the solutions are defined as a Filippov differential inclusion.
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Francis Mairet, Jean-Luc Gouzé. Control of a Bioreactor with Quantized Measurements. Fages, François and Piazza, Carla. Formal Methods in Macro-Biology, 8738, Springer International Publishing, pp.47-62, 2014, Lecture Notes in Computer Science, 978-3-319-10398-3. ⟨10.1007/978-3-319-10398-3_5⟩. ⟨hal-01092328⟩

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