A Comparison of Different Modelling and Simulation Approaches for Hybrid Dynamical Systems

Since 50 years the term hybrid system is a keyword in the field of modelling and simulation. Over the years many different formulations and structures were established to model hybrid systems and run their simulation. In general hybrid systems embrace different model behaviour to describe a process, mostly a mixture of discrete and continuous model structures. An example of this behaviour is the bouncing ball: The event of the ball reaching the ground has to be detected to enable the change in a model behaviour. This changing process is a hybrid system behaviour. In this paper three different descriptions and the established formalism for hybrid systems are compared. The different advantages and disadvantages of these formulations will be discussed. To analyse this in detail, all three formalisms will be applied on the bouncing ball example.