The Optimal Control Problems In Continuous Culture Fermentation

This paper uses the classic Monod growth model to study an optimal control problem in the continuous fermentation process. Firstly, we study a single popu-lation under a single substrate fermentation process. We fix the yield-maximizing as the optimal target. We get an optimal control problem with state constraints and prove that it is in fact an optimal control problem without constraints. Op-timal control theories show that an optimal solution for this problem exists and it should be a bang-bang control which can be determined by the conjugate vari-ables’symbol. In accordance with conditions on transversality condition, we can get the terminal value of the conjugate variable. By the symbolic function to express the optimal control, the problem transformed into a two point boundary value problem of differential equations. At last, we use the shooting method to give the numerical algorithms for solving the two point boundary value problem, and programming.We also study the process of fermentation in the process of a single substrate under a variety of groups and multi-substrate single-species competition mode. Synchronous growth model and the mutual inhibition model are studied. Finally, we also obtain optimal control for bang-bang control.