On the supervisory synthesis for distributed control of discrete event dynamic systems with communication delays

The supervisory control theory, first introduced by Ramadge and Wonham (1987), is based on an automata concept. The aim of this theory is to synthesize a supervisor in order to respect some logic specifications. Control systems, however, are often distributed, for quite obvious reasons of performance, fault tolerance, and distribution of sensors and actuators to different physical locations. Thus, an extension of Ramadge and Wonham theory to decentralized supervisory control is used. In this case, when data transmission between different sites takes a non null time, the case study is more crucial. Therefore, it proves that it is difficult, if not impossible, to know by common sense whether global functioning is correct in order to respect the specifications. In the paper, supervisor synthesis is based not only on the controllable events but also by introducing and determining time periods in control models. The role of these time periods is to absorb communication delays in such a way that these delays do not affect the role of the supervisor in respecting the specifications.