Controllability properties of a class of systems modeling swimming microscopic organisms

Mario Sigalotti (1, 2, 3) , Jean-Claude Vivalda (2, 3, 4)

1 IECN - Institut Élie Cartan de Nancy
2 CORIDA - Robust control of infinite dimensional systems and applications
3 INRIA Lorraine
4 LMAM - Laboratoire de Mathématiques et Applications de Metz

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, cosidered 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.

Domaines: Optimisation et contrôle [math.OC]

Mario Sigalotti, Jean-Claude Vivalda. Controllability properties of a class of systems modeling swimming microscopic organisms. 2007. ⟨hal-00188193v1⟩