Section:
New Results
Hybrid Modeling
Participants :
Albert Benveniste, Benoît Caillaud.
Hybrid system modelers have become a corner stone of complex embedded
system development. Embedded systems include not only control
components and software, but also physical devices. In this area,
Simulink is a de facto standard design framework, and Modelica a new
player. However, such tools raise several issues related to the lack
of reproducibility of simulations (sensitivity to simulation
parameters and to the choice of a simulation
engine). In [10] we propose using techniques
from non-standard analysis to define a semantic domain for hybrid
systems. Non-standard analysis is an extension of classical analysis
in which infinitesimal (the and in the celebrated
generic sentence ... of college
maths) can be manipulated as first class citizens. This approach
allows us to define both a denotational semantics, a constructive
semantics, and a Kahn Process Network semantics for hybrid systems,
thus establishing simulation engines on a sound but flexible
mathematical foundation. These semantics offer a clear distinction
between the concerns of the numerical analyst (solving differential
equations) and those of the computer scientist (generating execution
schemes). We also discuss a number of practical and fundamental issues
in hybrid system modelers that give rise to non-reproducibility of
results, non-determinism, and undesirable side effects. Of particular
importance are cascaded mode changes (also called "zero-crossings" in
the context of hybrid systems modelers). This work has taken place in
the framework of the Synchronics large scale
initiative (see section
8.1.1 ).
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