On the global controllability of Hamiltonian and other nonlinear systems: fountains and recurrence

In this paper a form of local accessibility for nonlinear control systems is introduced, called the continuous fountain condition. Subject to the condition that the states of a system are continuous fountains and one of various recurrence conditions holds, it is shown that the systems state space is (globally) controllable. These results are then applied to certain subsets of the state space of controlled Hamiltonian systems, called energy slices, in order to establish their controllability. The results in this paper have application to hybrid hierarchical control in that they give conditions for a finite analytic partition to satisfy the in-block controllability condition.