Supervisory Control of Time Petri Nets Using Net Unfolding

Abstract

We define supervisory controllers for enforcing deadlines on transition firings in time Petri nets. Given a target net transition t/sub d/, and a deadline /spl lambda/, we generate a controller that under broad assumptions forces t/sub d/ to fire every /spl lambda/ 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/sub d/. A transition is not allowed to fire when its latency is greater than the amount time left until t/sub d/ must fire. Our real-time supervisory controllers consist of two subnets, which are added to the controlled net in order to enforce deadline /spl lambda/ on the firing of t/sub d/. First, the clock subnet dynamically tracks the amount of time left until the expiration of /spl lambda/. 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/sub d/ has fired.