Reconfigurable Timed Extended Reachability Graphs for scheduling problems in uncertain environments

This paper aims to develop a new method to determine a robust scheduling control for systems evolving in uncertain environments. Time Petri Nets with controllable and uncontrollable transitions are used to model the system. The controllable transitions represent the operations and the uncontrollable transitions represent unexpected events that correspond either to interruption of operations or to unavailability of resources. The developed method computes reconfigurable control sequences based on the determination of series of timed extended reachability graphs (R-TERG). Once an unexpected event is detected, a reconfiguration point is created and the R-TERG is updated. Successive applications of the Dijkstra algorithm allow reconfiguring the control sequence in order to preserve optimality with respect to the faults that affect the system.