Toward the development of iteration procedures for the interval-based simulation of fractional-order systems

Rauh Andreas and Kersten Julia: Toward the development of iteration procedures for the interval-based simulation of fractional-order systems. In: Acta cybernetica, (25) 1. pp. 21-48. (2021)

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Abstract

In many fields of engineering as well as computational physics, it is necessary to describe dynamic phenomena which are characterized by an infinitely long horizon of past state values. This infinite horizon of past data then influences the evolution of future state trajectories. Such phenomena can be characterized effectively by means of fractional-order differential equations. In contrast to classical linear ordinary differential equations, linear fractional-order models have frequency domain characteristics with amplitude responses that deviate from the classical integer multiples of ±20 dB per frequency decade and, respectively, deviate from integer multiples of ± 2 in the limit values of their corresponding phase response. Although numerous simulation approaches have been developed in recent years for the numerical evaluation of fractional-order models with point-valued initial conditions and parameters, the robustness analysis of such system representations is still a widely open area of research. This statement is especially true if interval uncertainty is considered with respect to initial states and parameters. Therefore, this paper summarizes the current state-of-the-art concerning the simulation-based analysis of fractional-order dynamics with a restriction to those approaches that can be extended to set-valued (interval) evaluations for models with bounded uncertainty. Especially, it is shown how verified simulation techniques for integer-order models with uncertain parameters can be extended toward fractional counterparts. Selected linear as well as nonlinear illustrating examples conclude this paper to visualize algorithmic properties of the suggested interval-based simulation methodology and point out directions of ongoing research.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2021
Volume: 25
Number: 1
ISSN: 0324-721X
Page Range: pp. 21-48
Language: English
Publisher: University of Szeged, Institute of Informatics
Related URLs: http://acta.bibl.u-szeged.hu/73050/
DOI: 10.14232/actacyb.285660
Uncontrolled Keywords: Mittag-Leffler függvények, Differenciálegyenlet - frakcionális sorrendű, Picard iteráció
Additional Information: Bibliogr.: p. 44-48. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.02. Computer and information sciences
01. Natural sciences > 01.02. Computer and information sciences > 01.02.01. Computer sciences, information science and bioinformatics
Date Deposited: 2021. Jul. 19. 09:13
Last Modified: 2021. Jul. 19. 09:20
URI: http://acta.bibl.u-szeged.hu/id/eprint/73078

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