Towards Computational Hybrid System Semantics for Time-Based Block Diagrams

At the core of Model-Based Design, computational models have caused an autocatalytic trend to use computation in design by unlocking the potential of model transformations. Precisely specifying a computational transformation requires well-defined semantics of the source and target representations. In this regard, continuous-time behavior is an essential aspect of time-based block diagrams that is typically approximated by numerical integration. The corresponding theory, however, is mostly concerned with local error and the mathematical semantics of long time behavior fails to be sufficiently precise from a computational perspective. In this work, first a computational semantics is developed based on a multi-stage variablestep solver. Next, the computational semantics of the discrete and continuous parts of hybrid systems and their interaction are formalized in a unifying framework. The framework exploits a successful functional approach to defining discrete-time and discrete-event behavior established in other work. Unification is then achieved by developing a computational representation of the continuous-time behavior as pure functions on streams.