Constrained Controllability of Semilinear Delayed Systems

摘要

In the paper infinite-dimensional dynamical control systems described by semi-linear differential equations with delays in the state variables are considered. Using a general sufficient conditions for constrained exact controllability for infinite-dimensional dynamical systems sufficient conditions for constrained exact absolute local controllability are formulated and proved. It is generally assumed that the values of controls are in a convex and closed cone with vertex at zero. As an illustrative example, constrained exact absolute local controllability problem for semilinear dynamical system with one constant delay in the state variable is solved in details. Some remarks and comments on the existing results for controllability of nonlinear dynamical systems are also presented.