Open-loop optimization and trajectory tracking of a fed-batch bioreactor

This paper deals first with the open-loop optimization of a fed-batch bioreactor, using an approach combining direct transcription and collocation techniques. The proposed strategy avoids taking into account singular arcs as it transforms the optimization problem into a nonlinear programming problem (NLP). The state and control variables are both discretized and optimized through classical direct optimization methods. The optimal feeding law is thus computed being less sensitive to initialization of the algorithm. In a second time, the control law is synthesised to provide an optimal tracking of the previous trajectory. This is carried out using a linearizing state-feedback control in an inner loop, in addition to a controller in an outer loop to guarantee a good stability and accuracy. Finally, some numerical results on two case studies are given to illustrate the efficiency of the proposed optimisation and control strategies.