Constrained controllability of second order retarded nonlinear systems with nonlocal condition

In this paper, the constrained controllability of the second order retarded nonlinear systems with nonlocal condition has been established by using the theory of cosine families and the generalized open mapping theorem. A new set of sufficient conditions for the constrained controllability of retarded nonlinear systems is established under the assumption that the associated linear system is controllable. By using the Banach fixed point theorem, the existence of mild solution for the considered system with nonlocal delay condition has been deduced. Finally, an example is provided to verify the effectiveness of the obtained theory.