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**Optimal control of switched autonomous systems in microbial fed-batch cultures.**
*(English)*
Zbl 1213.82114

Summary: A switched autonomous system is proposed to formulate the fed-batch culture process by taking the switching instants between the feed and batch processes as control variables. To maximize the concentration of 1,3-propanediol (1,3-PD) at the terminal time, an optimal control model subject to our proposed switched autonomous system and continuous state inequality constraints is then presented. A computational approach is developed to find the optimal switching instants in two aspects. On the one hand, the constraint transcription and smoothing techniques are applied to dealing with the continuous state inequality constraints; on the other hand, the first and the second derivatives of the cost functional, where the transformed state constraints are treated as a penalty function, are derived by the calculus of variations. Numerical results show that, by employing the optimal switching instants, the concentration of 1,3-PD at the terminal time can be increased considerably.

### MSC:

82D60 | Statistical mechanics of polymers |

49J15 | Existence theories for optimal control problems involving ordinary differential equations |

49K15 | Optimality conditions for problems involving ordinary differential equations |

93C15 | Control/observation systems governed by ordinary differential equations |

93C95 | Application models in control theory |