Supervisory Controller Design for Timed-Place Petri Nets

Abstract

Supervisory controller design to avoid deadlock in discrete-event systems modeled by timed-place Petri nets (TPPNs) is considered. The recently introduced approach of place-stretching is utilized for this purpose. In this approach, given an original TPPN (OPN), a new TPPN, called the place-stretched Petri net (PSPN), is obtained. The PSPN has the property that its marking vector is sufficient to represent its state. By using this property, a supervisory controller design approach for TPPNs to avoid deadlock is proposed in the present work. An algorithm to determine the set of all the states of the PSPN which lead to deadlock is presented. Using this set, a controller for the PSPN is defined. Using this controller, a controller for the OPN is then obtained. Assuming that the given Petri net is bounded, the proposed approach always finds a controller in finite time whenever there exists one. Furthermore, this controller, when exists, is maximally permissive.