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XVI-ая конференция

Идентификация нелинейных систем в виде ядер Вольтерра с использованием данных импульсных откликов

Павленко В.Д., Массри М.М., Чернов Ю.В.

Одесский национальный политехнический университет, Украина,65044, Одесса, просп. Шевченко,1, +3(8-048) 762-84-79, E-mail: pavlenko_vitalij@mail.ru

1  стр. (принято к публикации)

The use of the mathematical models based on the Volterra integro-power series for identification of nonlinear dynamic systems is one of the long-standing problems of the control theory [1]. When determining the multidimensional Volterra kernels, however, the problems arise in separating the n-th order partial components from the measured system response to a given perturbation and then in determining the n-dimensional Volterra kernel. Solving these problems is computationally unstable, and this leads to significant identification errors even at small deviations (measurement noises) of initial input data. We have investigated the errors of identification of a nonlinear system in the form of the Volterra series with the use of testing impulse signals, basing on the separation of the partial components by differentiation of the system response with respect to the parameter-amplitude [2]. Computer experiments MATLAB on the choice of the test signal amplitude are performed and the results of identification of the Volterra kernels of the 1st, 2nd and 3rd orders are presented..Application of the noise suppression procedure based on the wavelet transformation to estimations of the Volterra kernels allows us to obtain smooth solutions and to lower the identification error 1.5÷3 times. The presented dependences of identification errors on the area of testing actions in determining the diagonal sections of the Volterra kernels allow us to specify the range of optimal amplitudes of pulse actions for different levels of response measurement errors which correspond to the minimal errors of identification of the Volterra kernels.


1.Giannakis G.B. and Serpedin E.A. Bibliography on Nonlinear System Identification and its Applications in Signal Processing, Communications and Biomedical Engineering // Signal Processing EURASIP, Vol. 81, No.3, Year 2001. Pp. 533-580.

2.Pavlenko V.D., Massri M.M., Chernov Y.V. Computing of the Volterra Kernels of a Nonlinear System Using Impulse Response Data // Proceedings of 9th International Middle Eastern Simulation Multiconference, MESM'2008, August 26–28, 2008, Philadelphia University, Amman, Jordan. Pp.131 – 138.

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