Non-constructive interval simulation of dynamic systems

Wei Pang, George M. Coghill, Allan M. Bruce

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Abstract

In this report, inspired by non-constructive simulation developed in the qual-
itative reasoning eld, we present a non-constructive interval simulation algorithm for
the simulation of dynamic systems. To perform this kind of simulation, we rst recast
two integration methods, which were originally used in traditional numerical simulation,
and made them suitable for performing interval simulation in a non-constructive man-
ner. Then we proposed an iterative interval narrowing algorithm to control the growth of
intervals during simulation. To achieve better accuracy and eciency of the simulation,
we designed several simulation modes to meet dierent requirements of various problems.
The proposed simulation algorithm was theoretically studied in terms of its completeness,
soundness, convergence, and stability. Finally two classical dynamic systems, as well as
an electrical circuit model containing an algebraic loop, were used as test examples to
demonstrate the validity of the proposed simulation approach.
Original languageEnglish
Place of PublicationAberdeen
PublisherDepartment of Computing Science, University of Aberdeen
Number of pages44
VolumeABDN–CS–12–02
Publication statusPublished - Jun 2012

Publication series

NameTechnical Report ABDN–CS–12–02

Keywords

  • qualitative reasoning
  • interval simulation
  • non-constructive simulation
  • interval analysis
  • Monte-Carlo simulation
  • Algebraic-loop model

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    Pang, W., Coghill, G. M., & Bruce, A. M. (2012). Non-constructive interval simulation of dynamic systems. (Technical Report ABDN–CS–12–02). Department of Computing Science, University of Aberdeen. http://homepages.abdn.ac.uk/pang.wei/pages/TechReport/abdntechrep12-02.pdf