Geometric and numerical methods in optimal control and applications to the swimming problem at low Reynolds number and to low thrust orbital transfer.

Jérémy Rouot 1
1 McTAO - Mathematics for Control, Transport and Applications
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : The work of this thesis falls within the geometric and numeric aspects of a problem of swimming at low Reynolds number for two models microswimmers: the recent Copepod model and the seminal three-link Purcell model. The cost to minimize is the mechanical power dissipated by the fluid viscous drag forces. This leads to a sub-Riemannian problem, which can be analyzed using tools of geometric optimal control theory. In parallel direct and indirect numerical schemes allow to perform numerical simulations, crucial to complete the theoretical study and to evaluate the optimal solutions. In a second part, we will focus on the time minimal orbital transfer problem with low thrust.
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Jérémy Rouot. Geometric and numerical methods in optimal control and applications to the swimming problem at low Reynolds number and to low thrust orbital transfer.. Optimization and Control [math.OC]. INRIA Sophia Antipolis, 2016. English. ⟨tel-01472370v1⟩

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