Stabilization of Hamiltonian systems perturbed by white noise

Optimal residence time control is studied as a measure of stabilization. Systems are considered with a control term scaling with the size of a small perturbing noise. The dynamics are shown to converge in a certain sense to a diffusion on a graph. Using the approach developed in Freidlin and Wentzell (1994, 1993) for random perturbations of Hamiltonian systems, a convergence theorem is discussed. An optimal control theorem is then developed to maximize the expected exit time from a domain