Mathematics – Optimization and Control
Scientific paper
2012-02-09
Mathematics
Optimization and Control
Scientific paper
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. Using an approximation method, we prove necessary optimality conditions in the form of Pontryagin 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.
Clement Frederique
Coron Jean-Michel
Shang Peipei
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