Supervisory control of time Petri nets using net unfolding

We define supervisory controllers for enforcing deadlines on transition firings in time Petri nets. Given a target net transition t_d, and a deadline λ, we generate a controller that under broad assumptions forces t_d to fire every λ time units. Our supervisory controller is based on the notion of transition latency. The latency of a net transition is an upper bound on the time between the firing of that transition and the firing of t_d. A transition is not allowed to fire when its latency is greater than the amount time left until t_d must fire. Our real-time supervisory controllers consist of two subnets, which are added to the controlled net in order to enforce deadline λ on the firing of t_d. First, the clock subnet dynamically tracks the amount of time left until the expiration of λ. As the deadline approaches, this subnet also indicates transitions that must be disabled because their latency has become greater than the time until the expiration of the deadline. When this happens, a supervisor subnet actually disables these transitions. These transitions are enabled again only after t_d has fired.