A linear optimal feedback control for producing 1,3-propanediol via microbial fermentation

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

Practical algorithm for stochastic optimal control problem about microbial fermentation in batch culture

How to add glycerol to maximize production of 1,3-propanediol (1,3-PD) is a critical problem in process control of microbial fermentation. Most of the existing works are focusing on modelling this process through deterministic-based differential equations. However, this process is not deterministic, but intrinsically stochastic considering nature of interference. Thus, it is of importance to consider stochastic microorganism. In this paper, we will modelling this process through stochastic differential equations and maximizing production of 1,3-PD is formulated as an optimal control problem subject to continuous state constraints and stochastic disturbances. A modified particle swarm algorithm through integrating the hybrid Monte Carlo sampling and path integral is proposed to solve this problem. The constraint transcription, local smoothing and time-scaling transformation are introduced to handle the continuous state constraints. Numerical results show that, by employing the obtained optimal control governed by stochastic dynamical system, 1,3-PD concentration at the terminal time can be increased compared with the previous results