Latency-Based Supervisors for Enforcing Deadlines in Time Petri Nets

We outline a supervisory control method for enforcing deadlines in real-time systems modeled as time Petri nets. Given a time Petri net Nscr_T, a net transition t_d, and a deadline d, we generate supervisory controllers that force t_d to fire at most d time units since the previous firing of t_d. Our method uses the unfolding of the ordinary (untimed) Petri net underlying Nscr _T in order to define control supervisors enforcing the deadline. The unfolding of a Petri net is an acyclic Petri net whose markings correspond to the markings of the original Petri net. An advantage of net unfoldings is that they show the causal relation among transition firings in the original Petri net. Using a net unfolding, we define a so-called latency for each transition in Nscr_T, which we assume to be live. The latency of a transition is an upper bound on the delay between the firing of that transition and the firing of t_d. Our supervisory controllers dynamically disable the firing of transitions whose latency is greater than the time left until the expiration of the deadline on t_d. Here we discuss the most crucial aspect of this method, namely the definition of transition latencies from net unfoldings