Karimov, Artur and Nepomuceno, Erivelton and Tutueva, Aleksandra and Butusov, Denis (2020) Algebraic Method for the Reconstruction of Partially Observed Nonlinear Systems Using Differential and Integral Embedding. Mathematics, 8 (2). pp. 1-22. ISSN 2227-7390

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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.

Item Type:	Article
Keywords:	nonlinear systems; nonlinear identification; system reconstruction; Buchberger–Möller algorithm; Laurent polynomials; nonlinear regression; memristor; chaotic system;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	16726
Identification Number:	https://doi.org/10.3390/math8020300
Depositing User:	Erivelton Nepomuceno
Date Deposited:	21 Nov 2022 16:12
Journal or Publication Title:	Mathematics
Publisher:	MDPI
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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