Seminar Details
2009-12-08 (14.00) : Modelling Competitive Coexistence in a Chemostat by LQ Type State Feedback
At Euler building
Organized by Mathematical Engineering
Speaker :
Charlotte Beauthier (FUNDP)
Abstract :
The chemostat model describes the interaction of microbial species which
are competing for a single nutrient. It has been used for different systems such
as lakes, waste-water treatment processes and biological reactors producing ge-
netically altered organisms. The competitive exclusion principle is a theoretical
result which states that the competition process yields at best a single winning
species in the long run. However, in nature, many species seem to coexist. This
contradiction between the theory and the real world is our main motivation for
modifying the model in order to try to bring them in better accordance.
In this talk, the problem is stated in terms of an LQ-optimal control problem
for a linearized system in order to garantee the coexistence of species for the
(nonlinear) chemostat model. Conditions are reported such that the computed
linear state feedback can be applied to the nonlinear system and garantee the
well-posedness of the model and in particular the coexistence of the species.
The results are illustrated by some numerical experiments.
This contribution is a joint work in progress with Joseph Winkin (FUNDP)
and Denis Dochain (UCL).