Constrained controllability

In the paper, infinite-dimensional, continuous-time control systems described by nonlinear and semilinear abstract differential equations are considered. Using methods of functional analysis sufficient conditions for constrained exact local 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. Illustrative application is also given. Moreover, some remarks and comments on controllability problems for nonlinear dynamical systems are presented.