卵泡排卵模型中细胞质量和成熟度的最优控制
Optimal control of cell mass and maturity in a model of follicular ovulation
摘要：
在本文中，我们研究与一个标量双曲型守恒律模型的卵泡发育的最优控制问题。卵泡细胞的年龄和成熟度的变化由2D守恒律描述，其中控制项作用于速度。控制问题在于优化卵泡细胞资源，使得卵泡成熟度在固定时间内达到最大值。在一个混合框架内，我们制定的最优控制问题，证明了必要的最优性条件的形式混合最大值原理。然后我们推导出最优策略，并证明至少存在一个具有单个切换时间的最优砰砰控制。
英文摘要：
In this paper, we study optimal control problems associated with a scalar hyperbolic conservation law modeling the development of ovarian follicles. Changes in the age and maturity of follicular cells are described by a 2D conservation law, where the control terms act on the velocities. The control problem consists in optimizing the follicular cell resources so that the follicular maturity reaches a maximal value in fixed time. Formulating the optimal control problem within a hybrid framework, we prove necessary optimality conditions in the form of Hybrid Maximum Principle. Then we derive the optimal strategy and show that there exists at least one optimal bang-bang control with one single switching time.
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