Control of stochastically perturbed self-oscillations

Control of the probabilistic distribution of the stochastic nonlinear self-oscillation cycle of a system to form a bundle of random trajectories with a given scatter about a deterministic limiting cycle is studied. A stochastic sensitivity function defining the Gaussian asymptote of the stationary distribution density is used a measure for the scatter. Complete controllability condition for a density cycle and optimal controller parameters are determined. The performance of designed methods is illustrated with an example on the design of controllers for a stochastically perturbed Brusselator.