Determination of Minimal Sets of Control Places for Safe Petri Nets

Our objective is to design a controlled system with a simple method for discrete event systems based on Petri nets. It is possible to construct the Petri net model of a system and the specification separately. By synchronous composition of both models, the desired functioning closed loop model is deduced. Often uncontrollable transitions lead to forbidden states. The problem of forbidden states is solved using linear constraints. A set of linear constraints allows forbidding the reachability of these states. Generally, the number of these so-called forbidden states and consequently the number of constraints are large and lead to a great number of control places. A systematic method to reduce the size and the number of constraints for safe Petri Nets is given. By using a method based on the Petri nets invariants, maximal permissive controllers are determined. The size of the controller is close to the size of the specified model, and it can be implemented on a PLC in a structural way.