Constrained exact controllability of semilinear systems

In the paper infinite-dimensional dynamical control systems described by semilinear 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 admissible controls are in a convex and closed cone with vertex at zero. Constrained exact local controllability of semilinear abstract second-order dynamical systems are also formulated and proved. As an illustrative example, constrained exact local controllability problem for semilinear hyperbolic type distributed parameters dynamical system is solved in details. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.