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S. Winkler, A. Körner, M. Bicher, F. Breitenecker:
"A Comparison of Different Modelling and Simulation Approaches for Hybrid Dynamical Systems";
Talk: UKSim2017-AMSS 19th Intl. Conference on Mathematical Modelling & Computer Simulation, Cambridge, United Kingdom; 2017-04-05 - 2017-04-07; in: "UKSim2017-AMSS 19th Intl. Conference on Mathematical Modelling & Computer Simulation", D. Al-Dabass, A. Orsoni, R. Cant, G. Jenkins (ed.); IEEE Computer Society Order Number E6161, 19/New York, USA (2017), ISBN: 978-1-5386-2735-8; 97 - 102.

Abstract-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.
I. INTRODUCTION
Nowadays Modelling and Simulation is used in nearly
every field of industry. Not only expensively manufactured
products are modelled and tested before produced but also
the production process itself is simulated in order to optimise
the work-flow and save money. Main motivation for
modelling and simulating is the attempt to optimise product
and process as much as possible. The moving motives of
course are money and time.
Hybrid systems are part of the research field modelling
and simulation. Although it is just part of this research area
hybrid systems are used to describe a variety of different
structures. This term always comes up if a simulation
contains discrete time events as well as continuous parts
[1],[2]. This terminology is very general and does not specify
if the hybrid approach is necessary due to model behaviour
or if the hybrid system just results due to simplifications of
the model for a certain period of time. Compared to that
hybrid systems can also be used to describe models with
different physical behaviour [8]. In this physical systems
the change in behaviour makes it impossible to use just one
model formulation or structure to implement it. Therefore
this kind of hybrid systems are also called variable structure
system [5].

http://dx.doi.org/10.1109/UKSim.2017.22