Nonlinear adaptive control for bioreactors with unknown kinetics

We consider a control problem for a single bioreaction occurring in a continuous and well-mixed bioreactor, assuming that the bioreaction's kinetics is not represented by a validated model. We develop a nonlinear controller and prove the global asymptotic stability of the closed-loop system towards the equilibrium corresponding to the set point. Since this control law needs the knowledge of some parameters, we derive an adaptive version of the nonlinear controller and prove again the global asymptotic stability of the closed-loop system. Finally, we show the relevance of our approach on a real-life wastewater treatment plant.