Supervisor Synthesis Using Labeled Petri Nets for Forbidden State Specifications

This research focuses on the forbidden state problem in the framework of labeled Petri nets (LPNs), i.e., to design a supervisor for a plant modeled by an LPN such that the closed-loop system cannot reach a set of predefined forbidden markings and does not contain any deadlock. Different from the traditional control scheme, the supervisor derived by this work can not only observe the observable transitions, but also the quiescence information. First, a new structure named an extended basis reachability graph (EBRG) is introduced to describe the reachability space of an LPN without computing all reachable markings. Based on an EBRG, a basis observer is then excogitated to represent the behavior of an LPN. Some states in the basis observer are defined as bad states and control-induced deadlocks, which relates to the undesirable behavior of the plant. Finally, an algorithm is introduced to compute a supervisor based on the basis observer. The consideration of system quiescence provides extra information on the marking estimation of the closed-loop system such that certain disabled transitions are re-enabled. Consequently, the developed supervisor in this article is generally more permissive than those do not observe the quiescence.