There Are no Hybrid Systems - A Multiple-Modeling Approach to Hybrid Modeling

There are no hybrid systems, there are only hybrid models. Whether or not a change is modeled as a continuous or discontinuous one, depends on the purpose of the model. A proper treatment of hybrid models is, hence, a matter of multiple modeling and model abstraction and approximation. More specifically, a proper theory of hybrid models has to be a theory of temporal (or behavioral) abstraction and approximation. The primary problem is: How and under which circumstances can we transform a continuous change into a discontinuous one and vice versa? The core of this question is whether or not a certain distinction is significant. This depends on the context which includes the overall system and the purpose of its modeling. The paper deals with the problem of deriving the sets of qualitative values of model variables that allow to generate the distinctions required by the goal of model based prediction and the structure of the system. We present a formal definition and analysis of the problem and an algorithm for computing appropriate qualitative values based on propagation of distinctions. We outline how this generic solution can be used for deriving models of time scale abstraction including discontinuous changes.