  We consider both the internal and boundary controllability problems for wave
equations under non-negativity constraints on the controls. First, we prove the
steady state controllability property with nonnegative controls for a general
class of wave equations with time-independent coefficients. According to it,
the system can be driven from a steady state generated by a strictly positive
control to another, by means of nonnegative controls, when the time of control
is long enough. Secondly, under the added assumption of conservation and
coercivity of the energy, controllability is proved between states lying on two
distinct trajectories. Our methods are described and developed in an abstract
setting, to be applicable to a wide variety of control systems.
