Cats do have control of their tails and use them as a form of communication. A cat often uses its tail to indicate to others what kind of mood it is in.
Cats that have their tails completely straight and in an upright position are often curious. Cats who have their tails straight but with a bit of a bend towards the top are often happy. These cats want people and other animals to come over and pet them or sit by them. Cats that are upset and irritated typically swish their tails back and forth quickly. They may also thump or hit their tails against furniture or the floor.