On control of stochastic sensitivity

Consideration was given to generation of the desired probabilistic characteristics of the attractors of the nonlinear stochastic control systems. In the case of small random perturbations, the scatter of trajectories in the neighborhood of stable equilibrium is describable in terms of the stochastic sensitivity matrix. Problem was posed of generating the desired stochastic sensitivity matrix. The corresponding notions of reachability and full controllability were examined. A criterion for full controllability was obtained, and a constructive description of the reachability set was given. Efficiency of the proposed constructions was demonstrated by way of example of control of the stationary distribution of the random states of the perturbed stochastic Van der Pol’s equation.