Optimal Control Problems Of Multistage Microbial Fermentation In Batch Culture

This dissertation takes the batch fermentation with the process of bioconversion glycerol to 1,3-propanediol by Klebsiella pneumoniae as the background. Based on the change of product concentration in the bioprocess, we consider two batch fermentation models and mainly study the optimal control problem about how to increase the yield intensity of 1,3-PD. By comparing the programming results with the real results, we can evaluate the models and the optimal algorithms more precisely, and provide theoretical reference for the industry of 1,3-PD production. Accordingly, this research can mean much in both theory and practice. The main contributions in this dissertation are summarized as follows:1. This dissertation is based on the process of bioconversion glycerol to 1,3-PD, we mainly consider how to increase the yield intensity of 1,3-PD. First we study the properties of the dynamical system and get an optimal control problem, then we transfer it into a series of approximation problems by using time-switch skills and smooth techniques. Moreover, we also prove that the two problems are equivalent.2. We used gradient method to solve the optimal problem in the early paper. Howev-er, the algorithm needs to solve state and costate differential equations together and the solution may be trapped at a local optimal solution. In this paper, we combine gradient method and particle swarm algorithm to calculate and get a global result.3. We also consider a two-stage model of batch culture in the final chapter. As it’s not differentiable, we adapt the Nelder-Mead simplex search method to solve the optimal control problem and have a better knowledge of how 1,3-PD changes during the fermentation.