On Reconstruction of Disturbances of a System of Differential Equations With Inaccurate Measurement of Part of the Coordinates

The article studies the problem of approximate online reconstruction of an unknown disturbance acting on a system described by ordinary differential equations. Under the assumption that some of the system coordinates are measured inaccurately, an algorithm for solving it is proposed, based on a combination of feedback control methods and methods of the theory of ill-posed problems. The convergence of the constructed approximations to the exact disturbance is established with appropriate matching of the measurement error and appropriately selected grids involved in the calculations.