Open AccessVerified Integration of Differential Equations with Discrete Delay
Author(s) -
Andreas Rauh,
Ekaterina Auer
Publication year - 2022
Publication title -
acta cybernetica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.143
H-Index - 18
eISSN - 2676-993X
pISSN - 0324-721X
DOI - 10.14232/actacyb.290904
Subject(s) - bounded function , ordinary differential equation , state (computer science) , delay differential equation , differential equation , state variable , population , mathematics , computer science , constant (computer programming) , control theory (sociology) , mathematical analysis , control (management) , physics , algorithm , demography , artificial intelligence , sociology , thermodynamics , programming language
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.