Abstract: Control and controllability of microscopic swimmers : theory and applications
At the microscopic scale, locomotion through a fluid follows different laws than at our scale, due to the predominance of the viscous effects (Stokes regime). The research on swimming micro-organisms and the design of swimming micro-robots is motivated in particular by biomedical applications, such as non-invasive surgery or delivery of a molecule to a precise location within the body. Of course, this requires the ability to propel and control these micro-robots precisely and efficiently. Mathematical control theory offers a good theoretical framework to address these issues. Thus, in this talk, I will present some results on controllability and control of microswimming robots. I will start by a short overview on controllability results for finite-dimensional systems. Then, moving towards applications, I will discuss the controllability and optimal control properties of model robots: a magneto-elastic swimmer, a system of two particles and a flow-controlled particle.