Optimality condition of the nonlinear impulsive system in fed-batch fermentation. (English) Zbl 1132.49029
Summary: Based on the nonlinear impulsive system of fed-batch fermentation, which is used in the process of bio-dissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae, this paper is concerned with the optimal control of the volumes of infused glycerol at impulsive moments. The optimal control model is developed. The authors study the properties of both the nonlinear impulsive system and the solution of it, and ascertain the existence of the optimal control. Then the optimality condition is obtained, which can be used as a necessary condition that the optimal control should satisfy.
MSC:
| 49N25 | Impulsive optimal control problems |
| 93C10 | Nonlinear systems in control theory |
| 92C45 | Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.) |
| 49K15 | Optimality conditions for problems involving ordinary differential equations |
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