Decentralized monitors design for Petri net models

The problem of designing an optimal decentralized supervisor that enforces static (e.g., job and resource bounds) and behavioral (e.g., liveness, reversibility and controllability) constraints simultaneously on a Petri net model is here addressed. The supervisor consists of multiple local controllers assigned to different control sites, such that each control site can operate on a subset of the net transitions. A transition can be employed by multiple sites, but is not necessarily controllable by all of them. The key elements of the approach are an integer linear programming formulation that finds the decentralized supervisor that maximizes the number of allowed states among a subset of those that would be allowed by a global supervisor and a branch & bound procedure on the state set that ultimately guarantees the maximal permissiveness of the solution.