Abstract
This paper is concerned with the design of an adaptive extremum seeking control scheme for a mass structured cell population balance model in a bioreactor. The feed substrate concentration is considered as the manipulated input to drive system states to the desired setpoints that maximize the value of an objective function of the cell density. We assume limited knowledge on the objective function and we use the substrate concentration measurements to estimate this function. We use the Lyapunov’s stability theorem and a persistency of excitation condition to show that the proposed adaptive extremum seeking control achieves the exponential convergence to the desired set points. Numerical simulation has been performed to illustrate the performance of the proposed approach.
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