External boundary control of the motion of a rigid body immersed in a perfect two-dimensional fluid

TL;DR

This paper demonstrates that through boundary control strategies, it is possible to steer a rigid body's motion within a bounded fluid domain from an initial to a final state without boundary contact, using impulsive boundary conditions.

Contribution

It introduces a boundary control method for the motion of a rigid body in a 2D perfect fluid, enabling precise maneuvering within a bounded domain.

Findings

Existence of boundary conditions that steer the rigid body to a desired final state.

The control strategy works within a finite positive time.

The method ensures the body does not touch the external boundary.

Abstract

We consider the motion of a rigid body due to the pressure of a surrounded two-dimensional irrotational perfect incompressible fluid, the whole system being confined in a bounded domain with an impermeable condition on a part of the external boundary. Thanks to an impulsive control strategy we prove that there exists an appropriate boundary condition on the remaining part of the external boundary (allowing some fluid going in and out the domain) such that the immersed rigid body is driven from some given initial position and velocity to some final position and velocity in a given positive time, without touching the external boundary. The controlled part of the external boundary is assumed to have a nonvoid interior and the final position is assumed to be in the same connected component of the set of possible positions as the initial position.