On Some Properties of Nonlinear Integral Models of Dynamic Processes

The paper presents algorithms for constructing dynamic models of technical (energy) systems in conditions of noisy data. We consider a class of nonlinear systems of Volterra-type integral equations of the first kind with an input signal consisting of two components. The problem of identifying the input signal of linear systems is well known when reduction to a system of equations of the second kind is performed by differentiating Volterra integral equations of the first kind. When constructing models, a control input action is formed that provides the specified response of the dynamic system. Identification algorithms based on the theory of Volterra polynomial equations are used. The paper considers the case with noisy initial data, including when the condition of non-degeneracy of matrices in front of the main part is violated at some fixed points in time.