Supervisory controller design to enforce some basic properties in timed-transition Petri nets using stretching

Supervisory controller design to enforce boundedness, reversibility, and liveness in timed-transition Petri nets with firing durations is considered. It is assumed that both controllable and uncontrollable transitions may be present and more than one transition may fire simultaneously. The approach of stretching is used to represent the state of the system. Algorithms are presented to design a supervisory controller using the forbidden states approach to enforce boundedness and reversibility simultaneously. The designed controller also guarantees T-liveness for the largest possible subset T of the set of transitions. In particular, boundedness, reversibility, and liveness are simultaneously enforced whenever it is possible. The designed controller is also the least restrictive controller which enforces boundedness and reversibility simultaneously.