Controller Design for Petri Net with Uncontrollable and Unobservable Transitions

Abstract

A controller design method for Petri net with uncontrollable and unobservable transitions that enforces the conjunction of a set of linear inequalities on the Parikh vector is proposed. The method is based on the theory that each place can be described with a Parikh vector inequality. Constraints are classified into admissible and inadmissible constraints. An inadmissible constraint cannot be directly enforced on a plant because of the uncontrollability or unobservability of certain transitions. Construct the controller though transforming the inadmissible constraint into admissible one. The method eases the design of controller, because it is based on part net design, and it only considers the direct or indirect transitions related to the constraints. So the computation required to find the Petri net controller is quite simple. Finally, the method is proved to be simple and efficient through one example.