Guaranteed Estimation of Solutions of First Order Linear Systems of Ordinary Differential Periodic Equations with Inexact Data from Their Indirect Noisy Observations

摘要

We consider first-order linear systems of ordinary differential equations with periodic coefficients. Supposing that right-hand sides of equations are not known and subjected to some quadratic restrictions, we obtain optimal, in certain sense, estimates of linear functionals defined on solutions to above-mentioned problems from observations of these solutions on a finite system of points and intervals. It is established that if correlation functions of observation errors are not known and belong to special sets, then linear guaranteed mean square estimates of linear functionals from solutions of considered problems are expressed via solutions of some systems of ordinary differential equations with periodic coefficients.