An extremum seeking approach via variable-structure control for fed-batch bioreactors with uncertain growth rate

• Extremum-seeking control approach for a class of fed-batch bioreactor with uncertain growth rate.
• Extremum-seeking controller based on sliding modes techniques.
• The controller scheme guarantees robustness against modeling errors, parametric variations and external perturbations.

In this paper, we present an extremum-seeking scheme based on an approach to variable structure control for fed-batch bioreactors. The proposed scheme deals with uncertainty on the specific growth rate without assuming an explicit mathematical expression. The control approach exploits the inhibitory effect of the substrate concentration on the growth rate, in such a manner that the closed-loop system reaches the sliding regime on an optimal switching manifold, which is defined by maximizing biomass production. The control scheme comprises an estimation scheme consisting of a high-gain observer and a discrete gradient estimator which computes the unknown terms. The practical stabilizability for the closed-loop system around an unknown optimal set-point is analyzed. Numerical experiments illustrate the effectiveness of the proposed approach.