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

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.