Delays Evaluation of Networked Control System Switches using Timed Coloured Petri Nets and Formal Series

In the field of automation systems, networked control systems in critical context must be temporally assess. To this end, the evaluation can be based on a reliable and well-defined graphical formalism. In this paper we propose the use of Timed Coloured Petri Nets to compute the maximal delay of a control network with switches. We introduce coloured formal series, an extension of formal series in the tropical algebra, to handle coloured models description by means of algebraic representations. These new representations are powerful as they can express linear coloured models behaviour as well as conflict resolution in the tropical algebra. They also yield functions to achieve automated temporal assessment.