Identification of Quadratic Volterra Polynomials in the “Input–Output” Models of Nonlinear Systems

Yury Voscoboynikov, Svetlana Solodusha, Evgeniia Markova, Ekaterina Antipina and Vasilisa Boeva
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Yury Voscoboynikov: Department of Applied Mathematics, Novosibirsk State University of Architecture and Civil Engineering, 630008 Novosibirsk, Russia
Svetlana Solodusha: Department of Applied Mathematics, Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia
Evgeniia Markova: Department of Applied Mathematics, Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia
Ekaterina Antipina: Department of Applied Mathematics, Melentiev Energy Systems Institute, Siberian Branch of Russian Academy of Sciences, 664033 Irkutsk, Russia
Vasilisa Boeva: Department of Applied Mathematics, Novosibirsk State University of Architecture and Civil Engineering, 630008 Novosibirsk, Russia

Mathematics, 2022, vol. 10, issue 11, 1-17

Abstract: In this paper, we propose a new algorithm for constructing an integral model of a nonlinear dynamic system of the “input–output” type in the form of a quadratic segment of the Volterra integro-power series (polynomial). We consider nonparametric identification of models using physically realizable piecewise linear test signals in the time domain. The advantage of the presented approach is to obtain explicit formulas for calculating the transient responses (Volterra kernels), which determine the unique solution of the Volterra integral equations of the first kind with two variable integration limits. The numerical method proposed in the paper for solving the corresponding equations includes the use of smoothing splines. An important result is that the constructed identification algorithm has a low methodological error.

Keywords: nonparametric identification; dynamic system; integral model; Volterra equations; smoothing cubic splines; selection of the smoothing option (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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