Solving inverse problems of dynamics of non-linear objects with the use of Volterra series

: pp.9-16
Kamyanets-Podilskyi Ivan Ohienko National University
Kamyanets-Podilskyi Ivan Ohienko National University
Norwegian University of Science and Technology

The article deals with the method of resolving inverse problems of dynamics of nonlinear dynamical objects described by the Volterra series. As an example the case of the Volterra series with two members has been considered. The proposed approach is based on the quadrature method. As a result the methods of resolving of Volterra polynominal integral equation of the first kind and second degree based on the left rectangle method and trapezoidal method were developed. Based on the offered approach, the software for restoration of signals of nonlinear dynamical objects was developed in the Matlab environment. The effectiveness of the means has been investigated in the course of the series of computing experiments including the possibility of their application while noise is superimposed on the input signal. Computational errors significantly depend on the type of the input signal, in particular for smooth signals the errors vary from 1% to 5% and with 10% of superimposednoise - to 15%.

Thus, the results of computing experiments have shown that the proposed method can be effectively used in the restoration of input signals of nonlinear dynamical systems described by the integro-powerVolterra series with two members.

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