A new method for the reconstruction of unknown non-monotonic growth functions in the chemostat

Jan Sieber (1) , Alain Rapaport (2, 3) , Mathieu Desroches (4) , Serafim Rodrigues (5)

1 EMPS - College of Engineering, Mathematics and Physical Sciences [Exeter]
2 MODEMIC - Modelling and Optimisation of the Dynamics of Ecosystems with MICro-organisme
3 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie
4 SISYPHE - SIgnals and SYstems in PHysiology & Engineering
5 CRNS - Centre for Robotics and Neural Systems

We propose an adaptive control law that allows one to identify unstable steady states of the open-loop system in the single-species chemostat model without the knowledge of the growth function. We then show how to use a continuation method to reconstruct the whole graph of the growth function. Two variants, in continuous and discrete time, are presented. The case of two species in competition is also examined.

Mots clés: chemostat; adaptive control; identification

Domaines: Optimisation et contrôle [math.OC]

Jan Sieber, Alain Rapaport, Mathieu Desroches, Serafim Rodrigues. A new method for the reconstruction of unknown non-monotonic growth functions in the chemostat. 2012. ⟨hal-00723246⟩