Efficient design of Petri-net supervisors with disjunctive specifications

The supervision based on place invariants is an efficient method for the supervision of Petri nets in which each inequality constraint is implemented by one monitor place. However, this method assumes specifications that describe convex legal sets. Non-convex legal sets can be described by disjunctions of inequality constraints. Specifications consisting of disjunctions of inequality constraints are called here disjunctive specifications. Previous work has shown that under certain boundedness assumptions it is possible to implement supervisors enforcing disjunctive specifications with conventional Petri nets. However, in the worst case, the number of places of the least-restrictive supervisors was exponentially related to the size of the specification. This paper introduces an enhanced approach that generates supervisors in which the number of places is linearly related to the size of the specification. The generated supervisors are least restrictive and are implemented with conventional Petri nets.