  We consider rare transitions induced by colored noise excitation in
multistable systems. We show that undesirable transitions can be mitigated by a
simple time-delay feedback control if the control parameters are judiciously
chosen. We devise a parsimonious method for selecting the optimal control
parameters, without requiring any Monte Carlo simulations of the system. This
method relies on a new nonlinear Fokker-Planck equation whose stationary
response distribution is approximated by a rapidly convergent iterative
algorithm. In addition, our framework allows us to accurately predict, and
subsequently suppress, the modal drift and tail inflation in the controlled
stationary distribution. We demonstrate the efficacy of our method on two
examples, including an optical laser model perturbed by multiplicative colored
noise.
