On the Soundness of Behavioural Abstraction in Hybrid Systems

We discuss the challenges of building a simulation framework for hybrid systems, in particular the well-known Zeno effect and correct composition of models idealised by abstracting irrelevant behavioural details (e.g. the bounce dynamics of a bouncing ball or the process of fuse melting in an electrical circuit). We argue that the cornerstone of addressing these challenges is the definition of a semantic framework with an appropriate underlying model of time. Using two simple examples, we illustrate the properties of such a model and explain why existing models are not sufficient. Finally, we propose a new Zeno-free semantic model that allows mixing discrete and continuous behaviour in a rigorous way and provides for the compositional behavioural abstraction. Although it is based on non-standard analysis, we explain how our semantic model can be used to develop hybrid system simulators.

Presented at:
2nd International Workshop on Simulation at the System Level, Cargese, Corsica., October 19-21, 2014
Invited talk

 Record created 2016-01-05, last modified 2018-11-14

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