Stochastic sensitivity synthesis in nonlinear systems with incomplete information

A problem of stabilizing stochastically forced equilibria in nonlinear dynamic systems with incomplete information is studied. A new control approach based on the idea of synthesizing a desired stochastic sensitivity for an equilibrium is developed. The focus is on the case when the system states are observed only partially, with noisy observations. For the task of control, a dynamic regulator composed by feedback and filter is used. The problem of synthesizing the assigned stochastic sensitivity by this dynamic regulator is then considered. For a general nonlinear system, an algebraic equation connecting the stochastic sensitivity matrix with parameters of the regulator is derived. For the important case of two-dimensional stochastic nonlinear oscillators, explicit formulas of the dependence of the stochastic sensitivity on the regulator parameters are obtained. These theoretical results are constructively applied to the stabilization of the randomly forced equilibrium of the van der Pol oscillator.