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.
- S. Odokyenko and N. Kostian, “Features of application of integrated models for the solution of inverse problems of dynamics”, Internet-Osvita-Nauka, pp. 138–140, Vinnytsia, Ukraine: Vinnytsya National University of Technology, 2014. (Russian)
- V. Salyha, et al., Automated process control systems. Identification and Optimal Control, Kharkiv, Ukraine: Vyshcha shkola, 1976. (Russian)
- S. Solodusha, “Simulation of automatic control systems based on Volterra polynomials”, Modeling and Analysis of Information Systems, vol. 1, no. 1, pp. 60–68, Yaroslavl, Russia: P.G. Demidov Yaroslavl State University, 2012. (Russian)
- S. Boyd, O. Chua, and C. A. Desoer, “Analytical foundations of Volterra series”, IMA Journal of Mathematical Control and Information, vol. 1, no. 3. pp. 243–284, 1984.
- V. Ivanyuk, V. Ponedilok, and V. Hryshchuk, “Computer realization deterministic method of identifying integrated models of nonlinear dynamic objects”, Mathematical and computer modelling. Series: Technical sciences, no. 10, pp. 59–67, Kamianets-Podilskyi, Ukraine: Kamyanets-Podilskyi Ivan Ohienko National University, 2014. (Ukrainian)
- V. Pavlenko, Identification of nonlinear dynamic systems in the form of Volterra kernels based on impulse response measurement data, Electronic Modeling, vol. 32, no. 3, pp. 3–18, Kyiv, Ukraine: Pukhov Institute for Modeling in Energy Engineering, 2010. (Russian)
- D. Sidorov, “Modeling of nonlinear nonstationary dynamical systems by Volterra series: identification and applications”, Sibirskiy Zhurnal Industrial'noi Matematiki, vol. 3, no. 1 (5), pp. 182–194, Novosibirsk, Russia: Sobolev Institute of Mathematics, 2000. (Russian)
- A. Verlan and V. Sizikov, Integral Equations: methods, algorithms, programs. Kyiv, Ukraine: Naukova dumka, 1986. (Russian)
- K. Pupkov, V. Kapalyn, and A. Yushchenko, Functional series in the theory of non-linear systems. Kyiv, Ukraine: Nauka, 1976. (Russian)