Optimal control of cell mass and maturity in a model of follicular ovulation

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 two-dimensional 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 the 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.