Optimal Estimation of Unknown Right-Hand Sides of First Order Linear Systems of Periodic Ordinary Differential Equations from Indirect Noisy Observations of Their Solutions

We consider first-order linear systems of ordinary differential equations with periodic boundary conditions and unknown right-hand sides which are subjected to some quadratic restrictions. From indirect noisy observations of their solutions on a finite system of points and intervals, under the assumption that correlation functions of observation errors are not known and belong to special sets, we obtain optimal, in certain sense, estimates of linear operators defined on right-hand sides of these equations.