| Summary: | 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.
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