From Physical Modelling to Compositional Models of Hybrid Systems

By a hybrid system we mean a discrete controller in interaction with a physical environment. This paper discusses methodologies for incorporating physically grounded models in representations of hybrid systems. To this end, we study a driver support system, an example which includes unmodelled inputs. We consider models at diierent levels of abstraction. First, we show that discrete models of the environment can be obtained from the continuous models without losing relevant information. We do this using an analysis of the continuous state space. We use Dynamic Transition Systems (DTS) for the modular modelling at this level of abstraction. Next, we consider models using Hybrid Transition Systems (HTS). This can be seen as a modular version of timed transition systems allowing both diierential and algebraic equations in each mode. Finally, we comment on expressivity requirements on hybrid formalisms for modelling realistic physical systems.