Controllability of Semilinear Dynamic Systems on Time Scales
In this paper, we study the controllability of semilinear systems on time scales. In order to do so, we first give a complete characterization for the controllability of linear systems on time scales in terms of surjective linear operators in Hilbert spaces. Second, we characterize the controllability of semilinear systems in terms of semilinear operators in Hilbert spaces as well. Third, we apply Banach fixed point theorem to prove the controllability of the semilinear control system on time scales assuming that the associated linear system is controllable and the nonlinear perturbation has a Lipschitz constant small enough.