A framework for controlling a nonlinear dynamical system against escap
e from a potential well is presented based on reducing the phase space
transport across the separatrix associated with the potential well. A
bandlimited open-loop control with finite lag is considered for syste
ms with weak additive stationary forcing including, specifically, the
colored Gaussian case. The related multiplicative, closed-loop control
problem is shown to reduce to an open-loop problem. A numerical examp
le based on the Duffing oscillator is presented to illustrate the theo
ry.