Output reference control for weight-balanced timed event graphs

Timed Event Graphs (TEGs) and their weighted extension WTEGs are particular timed Discrete Event Systems (DESs) where the dynamic behavior is described by synchronization and saturation effects. With dioids, a linear systems theory has been developed for (weighted) TEGs. In this paper, we use dioid theory to model the input-output behavior of a WTEG. Furthermore, we propose a control strategy which determines an optimal input for a predefined reference output. In this case, “optimal” means that input events are scheduled as late as possible with the restriction that the output events of the system do not occur later than specified by the reference. This strategy is often referred to as “just-in-time” control in literature.