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