Constrained controllability of semilinear systems with multiple delays in control

In the present paper finite-dimensional, stationary dynamical control systems described by semilinear ordinary differential state equations with multiple point delays in control are considered. Infinite-dimensional semilinear stationary dynamical control systems with single point delay in the control are also discussed. Using a generalized open mapping theorem, sufficient conditions for constrained local relative 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. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.