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ADAPTIVE ASYMPTOTIC STABILIZATION OF A BIOPROCESS MODEL WITH UNKNOWN KINETICS

The stability of a four-dimensional nonlinear model of a wastewater treatment process (proposed by Bernard, Hadj-Sadok, Dochain, Genovesi and Steyer in 2001) is studied. A feedback control law, depending only on on-line measurable quantities, is proposed. This feedback law stabilizes asymptotically the closed-loop system towards a previously chosen operating point. In order to prove that the closed-loop system is asymptotically stable, two Lyapunov-like functions are constructed explicitly. A numerical extremum seeking algorithm is then applied to stabilize the dynamics towards an equilibrium point corresponding to the maximum methane output flow rate. The robustness of the feedback is demonstrated by involving uncertainties in the growth rate model functions. Computer simulations are reported to illustrate the theoretical results.