Constrained controllability of semilinear systems

Abstract

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 a semilinear hyperbolic type distributed parameter dynamical system is solved in details. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.