Control of Equilibria for Nonlinear Stochastic Discrete-Time Systems

We consider a nonlinear discrete-time control system forced by stochastic disturbances. The problem addressed is a design of the feedback regulator that stabilizes an equilibrium of the closed-loop deterministic system and synthesizes a required dispersion of random states for corresponding stochastic system. To solve this problem we develop a method based on the stochastic sensitivity matrix technique. Main results of this technical note concern the synthesis of the stochastic sensitivity matrix, a geometric description of attainability set, and constructive design of regulator parameters. The effectiveness of the proposed approach is demonstrated on the stochastic Henon model. Using our technique we provide a low level of sensitivity for stochastically forced equilibria and suppress both regular and chaotic oscillations.