Conference article

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.

Hybrid Modeling Languages; Non-Standard Analysis; Models of Signals; Behavioral Abstraction; Operational Semantics