Optimal control theory and the efficiency of the swimming mechanism of the Copepod Zooplankton

Piernicola Bettiol (1) , Bernard Bonnard (2, 3) , Jérémy Rouot (3) , Alice Nolot (2)

1 LM-Brest - Laboratoire de Mathématiques
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 McTAO - Mathematics for Control, Transport and Applications

In this article, the model of swimming at low Reynolds number introduced by D. Takagi (2015) to analyze the displacement of an abundant variety of zooplankton is used as a testbed to analyze the motion of symmetric microswimmers in the framework of optimal control theory assuming that the motion occurs minimizing the energy dissipated by the fluid drag forces in relation with the concept of efficiency of a stroke. The maximum principle is used to compute periodic controls candidates as minimizing controls and is a decisive tool combined with appropriate numerical simulations using indirect optimal control schemes to determine the most efficient stroke compared with standard computations using Stokes theorem and curvature control. Also the concept of graded approximations in SR-geometry is used to evaluate strokes with small amplitudes providing a fixed displacement and minimizing the dissipated energy.

Mots clés: Low Reynolds number; Copepod swimmer; SR-geometry; Periodic optimal control; Transversality conditions

Domaines: Optimisation et contrôle [math.OC]

Piernicola Bettiol, Bernard Bonnard, Jérémy Rouot, Alice Nolot. Optimal control theory and the efficiency of the swimming mechanism of the Copepod Zooplankton. 2016. ⟨hal-01387423v1⟩