Optimal Control for Population Dynamics with Input Constraints in Chemostat Reactor Applications

Control strategies for chemostat-reactors are important for the synthesis of products with different applications. The yield depends on the age-structure of the population synthesizing the product. This structure can be influenced by the dilution rate. Modeling the population leads to a hyperbolic first-order PDE with integral boundary conditions. Both an Early- and a Late-Lumping approach are used to design optimal control strategies. To approximate the nonlinear system a Galerkin's approach is used with the eigenmodes of the linear steady-state system as ansatz functions. Through simulations both approaches are verified and compared. The control law arising from the Early-Lumping approach fits better to the simulated plant and leads to slightly better results due to its numerical conditions. Nevertheless, tracking is precise in both approaches while the input constraints are satisfied.