Introducing a New Mathematical Abstraction for Modeling Real Time Systems

Due to the increasing complexity of industrial production systems, there exists a need for the development of efficient formal approaches for their analysis and control. Various methods have been proposed and examined from researchers, without being widely adopted for direct industrial use. In general, an industrial production line can be modelled as a Discrete Event System, but a more accurate representation would result, if we considered it as a real-time system. This paper presents a new mathematical abstraction for modelling real-time systems. In comparison with the conventional methods, the proposed method introduces new formulation parameters and handles variables in a different manner. It gives the opportunity to handle both discrete and real valued variables as inputs, outputs or both. A formal definition of the method is given and computations or runs of two typical examples.