Approximate controllability of differential inclusions in Hilbert spaces

In this paper, controllability for the system originating from semilinear functional differential equations in Hilbert spaces is studied. We consider the problem of approximate controllability of semilinear differential inclusion assuming that semigroup, generated by the linear part of the inclusion, is compact and under the assumption that the corresponding linear system is approximately controllable. By using resolvent of controllability Gramian operator and fixed point theorem, sufficient conditions have been formulated and proved. An example is presented to illustrate the utility and applicability of the proposed method.