Skip to Main content Skip to Navigation
Master thesis

Contrôle optimal périodique : Applications à la dépollution de l'eau

Abstract : Periodic solutions of the chemostat model are studied under integral constraints on the washout rate, aiming at improving average water quality. For the one-species chemostat, an optimal control, which may admit a singular arc, is synthesized for convex-concave growth functions. The optimal trajectories generalize the existing ones for convex and concave growth functions. Then, unicity of periodic positive solutions is considered. In the two-species chemostat, a non-generic counterexample were infinitely many positive periodic solutions exist is constructed. In the one-species gradostat, unicity is proven for a rather broad class of configurations. Contrary to many existing results, this result applies for any monotonic growth function.
Complete list of metadata

Cited literature [54 references]  Display  Hide  Download
Contributor : Alain Rapaport <>
Submitted on : Wednesday, September 23, 2020 - 7:01:55 PM
Last modification on : Monday, January 25, 2021 - 1:18:01 PM
Long-term archiving on: : Friday, December 4, 2020 - 5:23:46 PM


Files produced by the author(s)


Public Domain


  • HAL Id : hal-02947280, version 1


Thomas Guilmeau. Contrôle optimal périodique : Applications à la dépollution de l'eau. Optimisation et contrôle [math.OC]. 2020. ⟨hal-02947280⟩



Record views


Files downloads