Optimal adaptive control of fed-batch fermentation processes with multiple substrates

We consider the optimization of fed-batch fermentation processes involving multiple limiting substrates for biomass growth, and possibly product synthesis, with respect to the volumetric feed rate of these substrates. Although analytical results obtained via application of the minimum principle are limited to low order processes, we illustrate how to exploit these results in characterizing nearly optimal control sequences in terms of the qualitative behavior of the specific rates for growth and production as functions of the limiting substrates. Furthermore, the deduced control sequences lead in a natural way to the design of optimal adaptive feedback controllers, which combine a nearly optimal performance with good robustness properties against modeling uncertainties and process disturbances