Modeling and optimal control of a nonlinear dynamical system in microbial fed-batch fermentation

  • Authors:

  • Chongyang Liu;Zhaohua Gong;Enmin Feng

  • Affiliations:

  • School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, PR China;School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, PR China;School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, PR China

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2011

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Abstract

The mathematical model and optimal control of microbial fed-batch fermentation is considered in this paper. Since it is decisive for increasing the productivity of 1,3-propanediol (1,3-PD) to optimize the feeding rate of glycerol and the switching instants between the batch and feeding processes in the fermentation process, we propose a new nonlinear dynamical system to formulate the process. In the system, the switching instants are variable and the feed rate of glycerol is regarded as the control function. Some important properties of the proposed system and its solution are then discussed. To maximize the concentration of 1,3-PD at the terminal time, an optimal control model involving the proposed system and subject to continuous state inequality constraints is established. The existence of the optimal control of the model is also proved. Finally, a computational approach is constructed on the basis of constraint transcription and smoothing approximation techniques. Numerical results show that the concentration of 1,3-PD at the terminal time can be increased considerably.