Structural method for supervisory control of discrete event within the framework of Petri nets: a one-to-one link between the supervisory control theory and the place invariant method

Abstract

ABSTRACT Several formal supervisory control methods for discrete event systems (DES) by Petri nets have been developed. However, they are partially structural because of the need to construct the reachability graph. Yet, the place invariant method is the simplest, although it does not guarantee an optimal solution in the presence of uncontrollability. To overcome this problem, we focus on the labelled PN (LPN), which offers a better structure for defining languages. This allowed us to establish a one-to-one link between the supervisory control theory and the place invariant method. This link is based on the definition of a structural condition of controllability of the LPN of closed loop DES. We have shown that the controllability condition, defined by the marking of places of the LPN is equivalent to the one defined by the LPN languages. Thus, we have been able to develop a structural method for supervisory control, without the construction of the reachability graph. This method is based on the structural determination of admissible constraints derived from the separator hyperplane of states space of the DES. Our approach gives the optimal solution (maximal permissive controller) in almost all of the real case studies considered.