Observer based extremum seeking control for cell population models with uncertain growth dynamics

In this work the optimal control problem of maximizing the cell production rate in chemostat reactors by manipulating the dilution rate under possibly time–varying uncertainties in the growth rate is addressed. Considering that the cell mass distribution is not an available measurement during cultivation, three estimation problems are formulated and addressed. Based on the respective observability property of each subsystem, extended Kalman filters are designed for the estimation of the gradient with respect to the input, uncertainties in the growth rate, and the cell mass distribution density function based on biomass measurements. Finally, the convergence of the proposed observers and optimal control strategy is tested in simulations.