We consider a finite-dimensional model for the motion of microscopic organisms whose propulsion exploits the action of a layer of cilia covering its surface. The model couples Newton's laws driving the organism, considered as a rigid body, with Stokes equations governing the surrounding fluid. The action of the cilia is described by a set of controlled velocity fields on the surface of the organism. The first contribution of the paper is the proof that such a system is generically controllable when the space of controlled velocity fields is at least three-dimensional. We also provide a complete characterization of controllable systems in the case in which the organism has a spherical shape. Finally, we offer a complete picture of controllable and non-controllable systems under the additional hypothesis that the organism and the fluid have densities of the same order of magnitude.

Classification: 37C20, 70Q05, 76Z10, 93B05, 93C10

Keywords: swimming micro-organisms, ciliata, high viscosity, nonlinear systems, controllability

@article{COCV_2010__16_4_1053_0, author = {Sigalotti, Mario and Vivalda, Jean-Claude}, title = {Controllability properties of a class of systems modeling swimming microscopic organisms}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {16}, number = {4}, year = {2010}, pages = {1053-1076}, doi = {10.1051/cocv/2009034}, zbl = {pre05821909}, mrnumber = {2744162}, language = {en}, url = {http://www.numdam.org/item/COCV_2010__16_4_1053_0} }

Sigalotti, Mario; Vivalda, Jean-Claude. Controllability properties of a class of systems modeling swimming microscopic organisms. ESAIM: Control, Optimisation and Calculus of Variations, Volume 16 (2010) no. 4, pp. 1053-1076. doi : 10.1051/cocv/2009034. http://www.numdam.org/item/COCV_2010__16_4_1053_0/

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