In this paper, we consider a multistage feedback control strategy for the production of 1,3-propanediol(1,3-PD) in microbial fermentation. The feedback control strategy is widely used in industry, and to the best of our knowledge, this is the first time it is applied to 1,3-PD. The feedback control law is assumed to be linear of the concentrations of biomass and glycerol, and the coefficients in the controller are continuous. A multistage feedback control law is obtained by using the control parameterization method on the coefficient functions. Then, the optimal control problem can be transformed into an optimal parameter selection problem. The time horizon is partitioned adaptively. The corresponding gradients are derived, and finally, our numerical results indicate that the strategy is flexible and efficient.
Bei, Honghan & Wang, Lei & Ma, Yanping & Sun, Jing & Zhang, Liwei. (2020). A linear optimal feedback control for producing 1,3-propanediol via microbial fermentation. Discrete and Continuous Dynamical Systems - Series S. Vol 13, no. 6.