We investigate the sensitivity behaviour and the controllability for an aerobic wastewater model. The problem is formulated as a nonlinear dynamical system. Using the tools of nonsmooth analysis, we firstly analyse the positivity and dissipation of the model. On the other hand, through the Gronwell’s inequality, we prove a sensitivity property of the model, quantified by the control parameters and initial conditions. This sensitivity leads to an error estimation between two trajectories. The strong controllability is investigated in a new setting: we assume that the recycle rate R, the residence time τ and the dissolved oxygen saturation concentration Cs are measurable time varying control functions. Hence, we reformulate the system as a nonlinear control problem. In this context and without linearising, we provide a strong controllability result with respect to the perturbations on initial conditions. As a consequence, we prove that an equilibrium point (when it exists) is locally controllable. Finally, we give some simulations illustrating our results.
@article{EP_2015_49_a11,
author = {M. Serhani and H. Boutanfit and A. Boutoulout},
title = {Sensitivity and {Strong} {Controllability} of a {Nonlinear} {Chemostat} {Model}},
journal = {ESAIM. Proceedings},
pages = {115--129},
year = {2015},
volume = {49},
doi = {10.1051/proc/201549010},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201549010/}
}
TY - JOUR
AU - M. Serhani
AU - H. Boutanfit
AU - A. Boutoulout
TI - Sensitivity and Strong Controllability of a Nonlinear Chemostat Model
JO - ESAIM. Proceedings
PY - 2015
SP - 115
EP - 129
VL - 49
UR - http://geodesic.mathdoc.fr/articles/10.1051/proc/201549010/
DO - 10.1051/proc/201549010
LA - en
ID - EP_2015_49_a11
ER -
%0 Journal Article
%A M. Serhani
%A H. Boutanfit
%A A. Boutoulout
%T Sensitivity and Strong Controllability of a Nonlinear Chemostat Model
%J ESAIM. Proceedings
%D 2015
%P 115-129
%V 49
%U http://geodesic.mathdoc.fr/articles/10.1051/proc/201549010/
%R 10.1051/proc/201549010
%G en
%F EP_2015_49_a11
M. Serhani; H. Boutanfit; A. Boutoulout. Sensitivity and Strong Controllability of a Nonlinear Chemostat Model. ESAIM. Proceedings, Tome 49 (2015), pp. 115-129. doi: 10.1051/proc/201549010
