From events to complex behaviors: a formal contribution to the requirement expression in Supervisory Control Theory

The Supervisory Control Theory (SCT) provides a formal framework for modeling Discrete-Event Systems (DES) and for controller synthesis, by distinguishing explicitly the non-controlled system from its specifications. Many extensions have been built on top of SCT, which continues to be extensively applied in the domain of DES design, and has given rise worldwide to many research projects. The events used as a central modeling artefact are the key to this success. However, the dynamics that can be modeled using SCT can only be designed in terms of event successions. This does not set a limit, in theory, but has leads to a practical drawback: expressing some specifications can become tedious. In this article we propose a new type of automata, meant to ease the expression of these specifications, while rigorously remaining within the discrete-event system control framework, relying on automata such as used by the Ramadge-Wonham theory.