The main question considered in control theory is the following: Given a system, is it possible to drive the system from any given initial state to any desired final state using a suitable control? In this talk, we will first present some applications of control theory and then briefly discuss the finite dimensional case. Next, we will consider this problem in the context of wave equations. One of the methods to solve control problems is to use Carleman estimates, which are weighted integral inequalities used to show unique continuation properties for partial differential equations. We will present some control results for wave equations obtained using suitable geometric Carleman estimates.
