Synthesis of petri net supervisors enforcing general constraints

Abstract

This paper deals with the synthesis of Petri net supervisor enforcing the more expressive constraints including marking terms, firing vector terms and Parikh vector terms. The method is developed to handle uncontrollable and unobservable transitions existing in the constraints. The “greater-than or equal” general constraints can also be transformed into “less-than or equal” Parikh constraints. An example is analyzed to show how the problem is solved. General constraint is first transformed into Parikh vector constraints, and Matrix-Transformation is proposed to obtain the admissible constraints without uncontrollable and unobservable transitions. Then the supervisor can be constructed based on constraints only consisting of Parikh vector terms. The method is proved to be more concise and effective than the method presented by Iordache and Moody especially when applied to large scale systems.