| Popis: |
The research deals with complete and approximate controllability of the system (∗) dx dy = f(t, x, u) , without control restraints to an arbitrary convex target set. First, some characterizations of complete controllability, to the target of (∗) and a special case of (∗) namely x = A(t)x + k(t, u) ∗∗ are given. As a consequence complete controllability is equivalent to null-controllability. Next certain equations are formulated. These are in the same spirit as J. P. Dauer's “A Controllability Technique for Nonlinear Systems” ( J. Math. Anal. Appl. oo (1972) , 442–451) and are utilized in the main contribution of the paper: Under certain convexity assumption, bounded perturbations of systems which are completely controllable to a fixed target G are completely controllable to G . Without the convexity assumption, but with perturbations satisfying a Lipschitz condition, approximate controllability to G of a perturbed system is equivalent to complete controllability to G of the unperturbed equation. |
