Summary: We give a sufficient conditions for the exact controllability of the non-linear generalized damped wave equation
on a Hilbert space. The distributed control and the operator is positive definite self-adjoint unbounded with compact resolvent. The non-linear term is a continuous function on and globally Lipschitz in the other variables. We prove that the linear system and the non-linear system are both exactly controllable; that is to say, the controllability of the linear system is preserved under the non-linear perturbation . As an application of this result one can prove the exact controllability of the sine-Gordon equation.