DETERMINING REGULAR ORBITS IN THE PRESENCE OF IRREGULAR TRAJECTORIES USING OPTIMAL-CONTROL THEORY

Two general algorithms are presented to determine regular orbits in the presence of irregular trajectories in a phase space of n degrees of freedom. The first algorithm searches for regular orbits with the energy as a free-floating parameter. The second algorithm seeks regular orbits at constant energy. These two approaches utilize optimal control theory to employ a small external control field that permits a search among the irregular motion for the regular orbits. The optimizing algorithm naturally seeks regular orbits with the control field turned off. Numerical results with a chaotic Hamiltonian show the method to be effective in determining regular trajectories. If the system is completely chaotic in some region, the method determines which initial condition is the best one in order to achieve a nearly regular orbit. (C) 1995 American Institute of Physics.