Monitor optimization in Petri net control

Deadlock Prevention and Liveness Enforcement in Petri nets are mostly addressed with monitor-based methods, designed indirectly using the concept of siphon or the theory of regions. The obtained control solutions are sometimes maximally permissive, but generally not optimal in terms of the number of monitors, nor in the cost of the control subnet. This paper proposes an optimization approach aiming at the direct design of the monitors, that allows for an easy formalization of the various control objectives. An efficient solution scheme, based on a branch-and-bound approach is also presented. The proposed monitor design algorithm yields significant improvements over known benchmark problems.