Consider a rigid body immersed in a viscous incompressible fluid. We begin this course with a brief analysis of the Stokes equations, which will be used to model the fluid flow. Then, motivated by applications in Naval Engineering and Military Engineering, for instance, we will address the following issues:

1. Boundary control problems: find the boundary values on the surface of the rigid body, in given control spaces, in order to (i) steer the solid into a prescribed velocity field; (ii) self-propel the body with maximal efficiency.

2. Inverse obstacle problem: determine the location and shape of the immersed object by means of stress measurements.