J. Botina et al., DETERMINING REGULAR ORBITS IN THE PRESENCE OF IRREGULAR TRAJECTORIES USING OPTIMAL-CONTROL THEORY, The Journal of chemical physics, 103(15), 1995, pp. 6637-6644
Two general algorithms are presented to determine regular orbits in th
e presence of irregular trajectories in a phase space of n degrees of
freedom. The first algorithm searches for regular orbits with the ener
gy as a free-floating parameter. The second algorithm seeks regular or
bits 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 algo
rithm naturally seeks regular orbits with the control field turned off
. Numerical results with a chaotic Hamiltonian show the method to be e
ffective in determining regular trajectories. If the system is complet
ely chaotic in some region, the method determines which initial condit
ion is the best one in order to achieve a nearly regular orbit. (C) 19
95 American Institute of Physics.