Enforcing Periodic Transition Deadlines in Time Petri Nets With Net Unfoldings
Haisheng Wang, Liviu Grigore, Ugo A. Buy, M. Lehene, Houshang Darabi · IEEE Transactions on Systems Man and Cybernetics - Part A Systems and Humans · 2010
We define a method for the automatic generation of supervisory controllers that force a plant to perform a given operation by a given deadline. The operation must be executed by a prespecified delay λ with respect to the previous execution of the operation. Although our supervisor generation occurs offline with respect to plant execution, the resulting controllers automatically take into account variable task durations in an effort to increase the flexibility of operation schedules in the controlled plant. We model both the controlled plant and control supervisors as time Petri nets. In this setting, our control supervisors must force a target transitiontdto fire within λ time units since the previous firing oftd. Our supervisor generation is based on the concept of a transition latency. The latency of a Petri net transitiontis the time interval during whichtmust be disabled in order for target transitiontdto fire by its deadline. If a transitiontthat may delay the firing oftdhas latencyl(t), thentmust be disabled at leastl(t) time units before the expiration of the deadline ontd. In this paper, we discuss in detail two algorithms for generating transition latencies, and we show an application to a maintenance system.