Constrained exact controllability of semilinear systems with delay in control

Abstract

In the paper infinite-dimensional dynamical control systems with constant point delay in the control 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 relative controllability of semilinear abstract second-order dynamical systems are also formulated and proved. As an illustrative example, constrained exact local relative controllability problem for semilinear hyperbolic type distributed parameters dynamical system is solved in details.