Constrained controllability of semilinear systems

In the paper infinite-dimensional stationary dynamical control systems described by semilinear abstract differential equations are considered. Using a generalized open mapping theorem, sufficient conditions for constrained exact controllability are formulated and proved. It is generally assumed that the values of controls are in a convex and closed cone with vertex at zero. As an illustrative example, constrained exact local controllability problem for semilinear retarded dynamical system is solved in detail. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.