  We derive a Hamiltonian control theory which can be applied to a 4D
symplectic map that models a ring particle accelerator composed of elements
with sextupole nonlinearity. The controlled system is designed to exhibit a
more regular orbital behavior than the uncontrolled one. Using the Smaller
Alignement Index (SALI) chaos indicator, we are able to show that the
controlled system has a dynamical aperture up to 1.7 times larger than the
original mode
