A Novel Approach to the Modeling and Control of Timed Event Graphs with Partial Synchronization

Abstract

Timed event graphs (TEGs) are a subclass of timed Petri nets whose dynamics is governed by standard synchronization, i. e., a transition is enabled to fire a certain time after the firing of some other transition(s) and is never disabled by the firing of other transitions. Partial synchronization (PS) imposes an additional condition: a partially synchronized transition can only fire within certain time windows determined by an external signal. Considering TEGs with PS allows to express time-varying behavior, which is manifested in several scenarios of practical relevance. We propose an original approach to model and control TEGs with PS, developed entirely within the domain of the dioid of counters, on which a well-consolidated control theory is available. Additionally, we show that our method can be combined with recent results and applied to the optimal control of TEGs with both PS and resource-sharing phenomena.