Geodesic
Sensitivity and Strong Controllability of a Nonlinear Chemostat Model
M. Serhani1 ; H. Boutanfit1 ; A. Boutoulout1
1 TSI Team, Faculty of Sciences, University Moulay Ismail, B.P.11201, Meknes, Morocco,
ESAIM. Proceedings, Tome 49 (2015), pp. 115-129.

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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.
DOI : 10.1051/proc/201549010

M. Serhani 1 ; H. Boutanfit 1 ; A. Boutoulout 1

1 TSI Team, Faculty of Sciences, University Moulay Ismail, B.P.11201, Meknes, Morocco, 
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     title = {Sensitivity and {Strong} {Controllability} of a {Nonlinear} {Chemostat} {Model}},
     journal = {ESAIM. Proceedings},
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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. http://geodesic.mathdoc.fr/articles/10.1051/proc/201549010/

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