Optimal control of nonlinear classical systems with application to unimolecular dissociation reactions and chaotic potentials

In this paper we apply optimal control theory to nonlinear classical systems for the design of electric fields that interact with the systems so that an ensemble of classical trajectories are manipulated in some desired way. Control of selective unimolecular bond dissociation is demonstrated in the classical regime on a model linear triatomic molecule with spreading of the ensemble of trajectories held to a minimum for closer agreement between quantum and classical mechanics. Control was also demonstrated over trajectories in a highly chaotic two-dimensional system. It was found in the cases studied that a high degree of control was attained in situations where the dynamics are chaotic in the absence of a controlling field.