Emergent Models in the Theory of Hybrid Systems

 

Dr. Manuela L. Bujorianu, University Twente, NL

 

Abstract:

 

Using system dimensions, a term coined from aspect engineering, hybrid
systems (HS) can be defined as a mixture of two dimensions: mixture of
continuous and discrete dynamics.01 In the modern research for HS,
there are many other dimensions that are considered simultaneously:
concurrency, probability, mobility, hierarchical control,
architectural views (UML), and so on. This rich dimension integration
is necessary for accurately modeling phenomena in technology, biology,
physical environment and society. The formidable modeling power
achieved in this way pays back in complexity of formal
verification. In this talk, the author research on finding a balance
between modeling and verification in the area of hybrid systems will
be presented. In a basic classification of hybrid systems, proposed by
the author, HS split in two classes: Universal models: The model is
obtained through algebraic operations from formal models of each
dimension. Emergent models: The model results by considering emerging
properties resulted from the interaction between different system
dimensions.

 

The models in the first class have been investigated using formal
tools from abstract algebra. Their main advantage resides from
compositionality which allows the extension of existing verification
methods.  For the models in the second class, the main advantage comes
from the possibility to define subtle and flexible relationships in
modeling, and the disadvantage is that new verification methods must
be designed from scratches.

 

A typical example for emergent models are the stochastic hybrid
systems. These models result from a deep interaction of traditional
academic disciplines like computing, mathematics and control
engineering.  An example of emerging properties is the stochastic
dependence between the probabilities associated with different
dimensions. Moreover, the emerging properties can have an impact on
system analysis that makes necessary a new classification, proposed by
the author: transitional and behavioral models. Behavioral modeling
and verification constitute newly introduced computational paradigms
that will be presented in the talk. Examples include Hilbertian formal
methods, stochastic reachability and functional abstractions. In the
end, possible applications in emergent and ubiquitous computing will
be discussed.