Constrained controllability of nonlinear systems

In the paper, infinite-dimensional dynamical systems described by nonlinear abstract differential equations are considered. Using a generalized open-mapping theorem 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 the vertex at zero. As an illustrative example. the constrained exact local controllability problem for nonlinear delayed dynamical system is solved in detail. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.