Gradient method optimization of penicillin production

A fermentation process is generally defined as a biological process containing the growth of the biomass (bacteria, yeasts) resulting from the consumption of essential substrate supplies (source of carbon, nitrogen, oxygen, etc.). The biomass growth is usually followed by the production of various products from which especially the variety of antibiotics makes the fermentation processes attractive for the industrial utilization. However, the complicated dynamics, high level of uncertainty and nonlinearity and difficult online measurement of the process variables come hand in hand with the attractivity and turn the attempts on optimal control of the fermentation process into a very delicate challenge. To tackle it, the theory of the gradient projection method has been partially adapted and fully implemented by the authors of this paper. Numerical experiments show its significantly better performance than for other known methods. Moreover, these experiments reveal an interesting “superprofile” visible for long cultivation times.