特征结构连续流培养模型中最小时间控制问题的目标可控性
Target controllability for a minimum time problem in a trait-structured chemostat model
AI总结：
本文研究了特征结构连续流培养模型中最小时间控制问题的目标可控性，通过分析辅助连续流型控制和反馈律，证明了解收敛到稳态，并展示了最优控制的存在性。
摘要：
在本文中，我们考虑由包含突变和一种限制性底物的特征结构连续流培养模型所 governed 的最小时间控制问题。我们的第一个主要结果证明了控制到状态映射的良态性。随后，我们分析了辅助连续流型控制、设计用于调节底物浓度的反馈律，并证明了相应的解收敛到系统的稳态。这些收敛结果用于展示达到对应于选择具有低加权平均半饱和常数的种群的目标集的可达性。最后，我们展示了达到目标集的最小时间问题关联的最优控制的存在性。这些理论发现通过数值模拟得以完成。
英文摘要：
In this paper, we consider a minimum time control problem governed by a trait-structured chemostat model including mutation and one limiting substrate. Our first main result proves the well-posedness of the control-to-state mapping. We subsequently analyze the class of auxostat-type controls, feedback laws designed to regulate substrate concentration, and prove that the corresponding solutions converge to a stationary state of the system. These convergence results are used to show the reachability of a target set corresponding to the selection of a population with a low weighted averaged half-saturation constant. Finally, we show the existence of an optimal control for the minimum time problem associated with reaching the target set. These theoretical findings are completed by numerical simulations.
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