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  • 标题:Non-Standard Analysis for Regularization of Geometric-Zeno Behaviour in Hybrid Systems
  • 本地全文:下载
  • 作者:Ayman Aljarbouh ; Muhammad Fayaz ; Muhammad Shuaib Qureshi
  • 期刊名称:Systems
  • 电子版ISSN:2079-8954
  • 出版年度:2020
  • 卷号:8
  • 期号:2
  • 页码:15-26
  • DOI:10.3390/systems8020015
  • 出版社:MDPI Publishing
  • 摘要:Geometric-Zeno behaviour is a highly challenging problem in the analysis (including simulation) of hybrid systems. Geometric-Zeno can be defined as an infinite number of discrete mode switches in a finite time interval. Typically, for hybrid models exhibiting geometric-Zeno, the numerical simulation either halts or produces false results, because an infinite number of discrete events occur in a given simulation time-step. In this paper, we provide formal methods for regularization of geometric-Zeno behaviour by using a non-standard analysis. In particular, we provide formal conditions for the existence of geometric-Zeno in hybrid systems, and we propose methods to allow geometric-Zeno executions to be continued beyond geometric-Zeno limit points. The concepts are illustrated with a case study throughout the paper.
  • 关键词:simulation; modelling; hybrid systems; geometric-Zeno; non-standard analysis simulation ; modelling ; hybrid systems ; geometric-Zeno ; non-standard analysis
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