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Efficiency Study of the Regularized Method of Identification Nonlinear Systems in the form of Volterra Kernels

Pavlenko S.V., Romanov D.Yu.

Яндекс.Переводчик translate.yandex.ua с русского ↔ на английский Одесский национальный политехнический университет, Украина, 65044, г. Одесса, просп. Шевченко, 1. Тел.: Odessa national Polytechnic University, Ukraine, 65044, Odessa, Av Shevchenko, 1. Tel: Яндекс.Переводчик translate.yandex.ua с русского ↔ на английский Одесский национальный политехнический университет, Украина, 65044, г. Одесса, просп. Шевченко, 1. Тел.: Odessa national Polytechnic University, Ukraine, 65044, Odessa, Avenue Shevchenko, 1. Tel: Яндекс.Переводчик translate.yandex.ua с русского ↔ на английский Одесский национальный политехнический университет, Украина, 65044, г. Одесса, просп. Шевченко, 1. Тел.: Odessa national Polytechnic University, Ukraine, 65044, Odessa, Avenue Shevchenko, 1. Tel: Яндекс.Переводчик translate.yandex.ua с русского ↔ на английский Одесский национальный политехнический университет, Украина, 65044, г. Одесса, просп. Шевченко, 1. Тел.: Odessa national Polytechnic University, Ukraine, 65044, Odessa, Avenue Shevchenko, 1. Tel: Яндекс.Переводчик translate.yandex.ua с русского ↔ на английский Одесский национальный политехнический университет, Украина, 65044, г. Одесса, просп. Шевченко, 1. Тел.: Odessa national Polytechnic University, Ukraine, 65044, Odessa, Avenue Shevchenko, 1. Tel,: +3 (0063) 461–74–72, psv85@yandex.ru

Investigated regularized method of deterministic identification of nonlinear dynamic systems (NDS) based on Volterra models in time domain [1]. As a test of the effects used irregular sequence of pulses. In contrast to the interpolation method of identification [2], where for numerical differentiation of responses on amplitude of test signals used formula in finite differences with fixed number of experimental studies of object identification in [1] is proposed to solve the Volterra integral equation of the 1st kind. However, for numerical implementation of the equations can be used unlimited on top of the number of experiments that can improve the accuracy of the computation of the derivatives, and, consequently, the accuracy of the identification.

The aim of this work is the analysis of the accuracy and numerical stability of a regularized method of identification of the NDS in the form of the Volterra kernels, based on the allocation of partial components by the procedure of differentiation of the feedback parameter is the amplitude of the test signals.

Developed software tools on the platform of Matlab that implement computational algorithms regularized method of identification NDS. The stability of the computational process of the identification procedure is provided by using the method of regularization of ill-posed problems A.N. Tikhonov. To smoothing of the estimates of the Volterra kernels it is used procedure noise reduction based on wavelet transform [1].

Obtained for test system using computer simulation estimation of the diagonal section of the 2-th order Volterra kernel are inaccurate in 2-4 times less than in the application of the interpolation method of identification [2].

References

1. Pavlenko S.V., Pavlenko.V.D. Regularization procedure of the identification nonlinear systems in the form of Volterra models [Electronic resource] // System Identification and Control Problems: Proceedings of the X International conference SICPRO’15, January 26-29, 2015, Moscow, V.A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences. – М.: ICS RAS, 2015. – С. 230-238. – ISBN 978-5-91450-162-1

2. Pavlenko V., Pavlenko S., Speranskyy V. Chapter 10: Identification of systems using Volterra model in time and frequency domain // In book: «Advanced Data Acquisition and Intelligent Data Processing». V. Haasz and K. Madani (Eds.) – River Publishers, 2014. – P.233-270. – ISBN 978-87-93102-73-6

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