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**Optimal control of a fed-batch fermentation involving multiple feeds.**
*(English)*
Zbl 1242.49087

Summary: A nonlinear dynamical system, in which the feed rates of glycerol and alkali are taken as the control functions, is first proposed to formulate the fed-batch culture of 1,3-propanediol (1,3-PD) production. To maximize the 1,3-PD concentration at the terminal time, a constrained optimal control model is then presented. A solution approach is developed to seek the optimal feed rates based on control vector parametrization method and improved differential evolution algorithm. The proposed methodology yield an increase by 32.17% of 1,3-PD concentration at the terminal time.

### MSC:

49N90 | Applications of optimal control and differential games |

49M30 | Other numerical methods in calculus of variations (MSC2010) |

### Keywords:

nonlinear dynamical system; feed rates of glycerol and alkali; constrained optimal control model; control vector parametrization metho; improved differential evolution algorithm
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\textit{C. Liu} et al., J. Appl. Math. 2012, Article ID 245315, 13 p. (2012; Zbl 1242.49087)

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### References:

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