Equations for the continuous estimation of the perturbations of dynamical systems

A dynamical system acted upon by external perturbations is considered. It is assumed that the phase state of the system (or a part of it) is observed with certain errors. The problem is to construct differential equations for estimating (reconstructing) the perturbations using measurement data. Unlike in papers in which cases of discrete instants of the observations are analysed, the continuous case is considered for which differential equations of an auxiliary system are derived, the controls in which are approximations of an unknown input. The general constructions are illustrated by means of an example.