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

• Published in: Mathematical and computer modelling Vol. 53; no. 1; pp. 168 - 178
• Main Authors: Liu, Chongyang, Gong, Zhaohua, Feng, Enmin
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2011; Elsevier
• Subjects: batch fermentation; Calculus of variations and optimal control; Constraint transcription; Exact sciences and technology; Fed-batch fermentation; Global analysis, analysis on manifolds; glycerol; Mathematical analysis; mathematical models; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Nonlinear dynamical system; Numerical analysis. Scientific computation; Optimal control; Sciences and techniques of general use; Switching instant; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Constraint transcription; Switching instant; Nonlinear dynamical system; Optimal control; Fed-batch fermentation; Smoothing methods; Approximation; Control system; Dynamical system; Non linear system; Scientific computation; Smoothing; Applied mathematics; Inequality constraint; Mathematical model; Computer aided analysis; State constraint
• ISSN: 0895-7177; 1872-9479
• DOI: 10.1016/j.mcm.2010.08.001

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.