Geodesic
Controllability properties of a class of systems modeling swimming microscopic organisms
ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1053-1076

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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.

DOI : 10.1051/cocv/2009034
Classification : 37C20, 70Q05, 76Z10, 93B05, 93C10
Keywords: swimming micro-organisms, ciliata, high viscosity, nonlinear systems, controllability 
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     title = {Controllability properties of a class of systems modeling swimming microscopic organisms},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1053--1076},
     publisher = {EDP-Sciences},
     volume = {16},
     number = {4},
     year = {2010},
     doi = {10.1051/cocv/2009034},
     mrnumber = {2744162},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2009034/}
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Sigalotti, Mario; Vivalda, Jean-Claude. Controllability properties of a class of systems modeling swimming microscopic organisms. ESAIM: Control, Optimisation and Calculus of Variations, Tome 16 (2010) no. 4, pp. 1053-1076. doi: 10.1051/cocv/2009034

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