Reconfigurable timed graphs for the design of optimal scheduling in uncertain environments based on transition-timed Petri net

This paper is about the design of firing sequences of minimal time for a class of timed discrete event systems that behave in uncertain environment including unexpected events. Such systems are modelled using partially controllable Transition-Timed Petri nets that encompass controllable deterministic, controllable stochastic and uncontrollable stochastic transitions. The main contribution of the work is to embed the timing aspects of such systems in Reconfigurable Timed Extended Reachability Graphs. As a consequence, the scheduling problem is solved with a standard optimization method. An application to the reactive scheduling of manufacturing systems highlights the advantages of the approach.