Deadlock Avoidance Controller Design for Timed Petri Nets Using Stretching

The recently introduced method, which was called "stretching," is extended to timed Petri nets which may have both controllable and uncontrollable transitions. Using this method, a new Petri net, called "stretched Petri net," which has only unit firing durations, is obtained to represent a timed-transition Petri net. Using this net, the state of the original timed Petri net can be represented easily. This representation also makes it easy to design a supervisory controller for a timed Petri net for any purpose. In this paper, supervisory controller design to avoid deadlock is considered in particular. Using this method, a controller is first designed for the stretched Petri net. Then, using this controller, a controller for the original timed Petri net is obtained. Algorithms to construct the reachability sets of the stretched and original timed Petri nets, as well as algorithms to obtain the controller for the original timed Petri net are presented. These algorithms are implemented using MATLAB. Examples are also presented to illustrate the introduced approach.