Regularization in the Problem of Minimization of Stochastic Sensitivity

Abstract

We consider a problem of the construction of feedback regulator which synthesizes the assigned stochastic sensitivity of the equilibrium in stochastically forced nonlinear dynamic system. In the case of complete information, it is shown that this problem can be reduced to the solution of the matrix algebraic equation. A presence of noise in measurements deforms the stochastic sensitivity. We find conditions when such deformation is extremely large, and the considered problem is ill-posed. For this ill-posed problem, a regularization method is suggested. We propose an analytical approach which allows us to take into account a presence of noise in measurements when we construct an optimal feedback regulator. General theoretical results are illustrated by examples. © 2018