[hal-01076688] Stabilization of a fluid-rigid body system

We consider the mathematical model of a rigid ball moving in a viscous incompressible fluid occupying a bounded domain Ω with an external force acting on the ball We investigate in particular the case when the external force is what would be produced by a spring and a damper connecting the center of the ball h to a fixed point h 1 ∈ Ω If the initial fluid velocity is sufficiently small and the initial h is sufficiently close to h 1 then we prove the existence and uniqueness of global in time solutions for the model Moreover in this case we show that h converges to h 1 and all the velocities of the fluid and of the ball converge to zero Based on this result we derive a control law that will bring the ball asymptotically to the desired position h 1 even if the initial value of h is far from h 1 and the path leading to h 1 is winding and complicated Now the idea is to use the force as described above with one end of the spring and damper at h while other end is jumping between a finite number of points in Ω that depend on h a switching feedback law



from HAL : Dernières publications http://ift.tt/1DDcnVq