Verified integration of differential equations with discrete delay

Rauh Andreas and Auer Ekaterina: Verified integration of differential equations with discrete delay. In: Acta cybernetica, (25) 3. pp. 677-702. (2022)

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Many dynamic system models in population dynamics, physics and control involve temporally delayed state information in such a way that the evolution of future state trajectories depends not only on the current state as the initial condition but also on some previous state. In technical systems, such phenomena result, for example, from mass transport of incompressible fluids through finitely long pipelines, the transport of combustible material such as coal in power plants via conveyor belts, or information processing delays. Under the assumption of continuous dynamics, the corresponding delays can be treated either as constant and fixed, as uncertain but bounded and fixed, or even as state-dependent. In this paper, we restrict the discussion to the first two classes and provide suggestions on how interval-based verified approaches to solving ordinary differential equations can be extended to encompass such delay differential equations. Three close-to-life examples illustrate the theory.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2022
Volume: 25
Number: 3
ISSN: 0324-721X
Page Range: pp. 677-702
Language: English
Publisher: University of Szeged, Institute of Informatics
Place of Publication: Szeged
Event Title: Conference of PhD Students in Computer Science (12.) (2020) (Szeged)
Related URLs:
DOI: 10.14232/actacyb.290904
Uncontrolled Keywords: Differenciálegyenlet - késleltetett, Differenciálegyenlet - dinamikus rendszer
Additional Information: Bibliogr.: p. 699-702. ; ill. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
01. Natural sciences > 01.02. Computer and information sciences
Date Deposited: 2022. May. 13. 10:02
Last Modified: 2022. May. 13. 10:02

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