DEVS as a common denominator for multi-formalism hybrid systems modelling

When modelling complex systems, complexity is usually not only due to a large number of coupled components, but also to the diversity of these components and to their intricate interactions. One would like to use a variety of formalisms to “optimally” describe the behaviour of different system components, aspects, and views. The choice of appropriate formalisms depends on criteria such as the application domain, the modeler´s background, the goals, and the available computational resources. In the article, a formalism transformation graph (FTG) is presented. In the FTG, vertices correspond to formalisms, and edges denote existing formalism transformations. A transformation is a mapping of models in the source formalism onto models in the destination formalism (with behaviour invariance). This traversal allows for meaningfully coupling models in different semantics. Once mapped onto a common formalism, closure under coupling of that formalism makes the meaning of the coupled model explicit. In the context of hybrid systems models, the formalism transformation converges to a common denominator which unifies continuous and discrete constructs. Often, this is some form of event-scheduling/state-event locating/DAE formalism and corresponding solver. A different approach is presented which maps all formalisms, and in particular continuous ones, onto Zeigler´s DEVS. Hereby, the state variables of the continuous models are discretized rather than time and the DEVS transition function progresses from one discretized state value to either the one just above or the one just below, giving as output, the time till the next transition