Abstract
Considering both extracellular and intracellular environments, we propose a nonlinear switched system composed of 16 modes based on the different metabolic mechanism to model the microbial continuous fermentation process of glycerol to 1,3-propanediol (1,3-PD). The existence and continuity of sensitivities of the system states with respect to the decision variables and unknown parameters are discussed. Taking the dilution rate and the feeding glycerol concentration as control variables, the sensitivity functions as constraints, an optimal control problem is presented with the concentration of 1,3-PD at the terminal time as performance index. According to sensitivity analysis, we obtain the gradient formulas of performance index and constraints with respect to the decision variables and the parameters to be identified. The sequential quadratic programming algorithm is adopted to seek a numerical solution. Numerical results indicate that under the obtained optimal dilution rate and feeding glycerol concentration, the productivity of 1,3-PD at the terminal time is increased significantly.
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