Abstract
We consider the problem of optimal control of large fluctuations. Our approach is based on the concept of the optimal fluctuational path along which the system is most likely to move when it fluctuates to a given state. Optimal control requires double optimization: over realizations of the control field and fluctuational paths. We formulate the appropriate variational problem. Using a white-noise-driven dynamical system as an example, we show that even comparatively weak control fields, if applied in an optimal way, can exponentially strongly reduce the probability of an undesirable fluctuation or increase the probability of a desirable one. Explicit expressions are obtained for the cases of control by a spatially uniform time-dependent field and by a stationary nonuniform field. We show that, in the problem of control, there generically occur singularities related to topological singularities found in the problem of large fluctuations. @S1063-651X~97!09203-9#
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