Deadlock characterization for Petri nets control using GMEC´s and observers

In this paper we deal with the problem of controlling a Petri net whose marking cannot be measured but is estimated using an observer. The control objective is that of enforcing a set of generalized mutual exclusion constraints (GMEC) and all the transitions are assumed to be controllable. Clearly, the use of marking estimates may significantly reduce the performance of the closed-loop system and may lead to a deadlock. If the net times out, i.e., if no transition firing occurs within a reasonable amount of time in the controlled system, an efficient procedure may be invoked to recover the net from a controller induced deadlock. The novel contribution of this paper is that of exploring in detail the characterization of those cases in which the proposed recovery procedure works.