Identification of oscillatory systems with unknown continuous input actions

The paper considers the problem of identifying a non-autonomous nonlinear system of ordinary differential equations by use of time series of observed variables. Identification of non-autonomous system was done by multiple use of autonomous system identification method within moving window. As a result, unknown structure of equations, values of constant coefficients, and time series of variable input actions of the system under study were found. It has been analytically and experimentally shown that there can be a time shift between the results of the numerical identification and the true values of input actions. The proposed method does not impose restrictions on the number of input actions in the system under the study, and even allows to identify the system with all coefficients that are time dependent. The condition for the applicability of the method is the low rate of change of input actions.