  This thesis addresses the problem of developing a quantum counter-part of the
well established classical theory of control. We dwell on the fundamental fact
that quantum states are generally not perfectly distinguishable, and quantum
measurements typically introduce noise in the system being measured. Because of
these, it is generally not clear whether the central concept of the classical
control theory -- that of observing the system and then applying feedback -- is
always useful in the quantum setting. We center our investigations around the
problem of transforming the state of a quantum system into a given target
state, when the system can be prepared in different ways, and the target state
depends on the choice of preparation. We call this the "quantum tracking
problem" and show how it can be formulated as an optimization problem that can
be approached both numerically and analytically. This problem provides a simple
route to the characterization of the quantum trade-off between information gain
and disturbance, and is seen to have several applications in quantum
information.
