Stochastic equilibria control and chaos suppression for 3D systems via stochastic sensitivity synthesis

In this paper, we consider a nonlinear controlled system forced by stochastic disturbances. The problem addressed is to design a feedback regulator that can stabilize an equilibrium of the closed-loop system and, around this equilibrium, to synthesize a required dispersion of random states of the corresponding system. We use a stochastic sensitivity function technique to approximate the stationary probabilistic distribution of these random states. We also develop a new method for stabilization based on the stochastic sensitivity synthesis. A constructive description of the attainability set of the stochastic sensitivity matrices for a 3D system is given. The effectiveness of the new approach is demonstrated by the 3D stochastic Chen system. It is shown that the new regulator provides a low level of sensitivity and can suppress both regular and chaotic oscillations.