A control policy for γ-nets without reachability analysis and siphon enumeration

Synthesizing maximally permissive controllers with fewest monitors has been a popular research topic. Current optimal controllers for large flexible manufacturing systems (FMS) require costly time consuming reachability analysis. Our previous work shows that among all n-dependent siphons, only one siphon (whose unmarked state follows specific token distribution) needs to be controlled. This greatly simplifies the synthesis as well as minimizes the number of monitors required while making the controlled net nearly maximally permissive. However, some live states may get lost. To reach more live states, the controller regions must be refined to be less affected or disturbed by the monitors and their controlled arcs. We observe that the markings of all the resulting controller regions follow a simple pattern. Based on this pattern of unmarked siphons, this paper further proposes a maximally permissive control policy for a subclass of S³PR (Systems of Simple Sequential Processes with Resources).