Numerical approximation of optimal control of biochemical reactors

The engineering approach to biochemical reaction engineering is based on mathematical modelling of microorganism metabolism, biomass growth, and heat and mass transport mechanism. Microbial processes are intrinsically very complex, and are the result of interaction of physical processes, and microorganism activity as a function of the total, highly complex, biochemical synthesis. The complexity of the microbial processes offers to engineers a number of opportunities for improvement and optimization of industrial processes involving microorganisms. The multiple complexity of interactions and the adaptive nature of microorganisms limits the modelling to a rather restricted state space of process variables and parameter values. Usually the models are combinations of basic mass and energy balances combined with regression models for parameters, such as yield, maintenance, and saturation coefficients. Therefore, the mathematical approach to optimisation has to bear with severe constraints due to the limited domain of model applicability. The paper presents a numerical method based on approximation of the optimal control and the state functions by polynomials.