Algebraic Method for the Reconstruction of Partially Observed Nonlinear Systems Using Differential and Integral Embedding

Artur Karimov, Erivelton G. Nepomuceno, Aleksandra Tutueva and Denis Butusov
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Artur Karimov: Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, Saint Petersburg 197376, Russia
Erivelton G. Nepomuceno: Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of São, João del-Rei, São João del-Rei MG 36307-352, Brazil
Aleksandra Tutueva: Department of Computer Aided Design, Saint Petersburg Electrotechnical University “LETI”, Saint Petersburg 197376, Russia
Denis Butusov: Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, Saint Petersburg 197376, Russia

Mathematics, 2020, vol. 8, issue 2, 1-22

Abstract: The identification of partially observed continuous nonlinear systems from noisy and incomplete data series is an actual problem in many branches of science, for example, biology, chemistry, physics, and others. Two stages are needed to reconstruct a partially observed dynamical system. First, one should reconstruct the entire phase space to restore unobserved state variables. For this purpose, the integration or differentiation of the observed data series can be performed. Then, a fast-algebraic method can be used to obtain a nonlinear system in the form of a polynomial dynamical system. In this paper, we extend the algebraic method proposed by Kera and Hasegawa to Laurent polynomials which contain negative powers of variables, unlike ordinary polynomials. We provide a theoretical basis and experimental evidence that the integration of a data series can give more accurate results than the widely used differentiation. With this technique, we reconstruct Lorenz attractor from a one-dimensional data series and B. Muthuswamy’s circuit equations from a three-dimensional data series.

Keywords: nonlinear systems; nonlinear identification; system reconstruction; Buchberger–Möller algorithm; Laurent polynomials; nonlinear regression; memristor; chaotic system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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