Sensitivity and Strong Controllability of a Nonlinear Chemostat Model

Abstract

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 rstly 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, quantied 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 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. R esum