Approximated timed reachability graphs for the robust control of discrete event systems

This paper is about control sequences design for Discrete Event Systems (DES) modeled with Time Petri nets (TPN) including a set of temporal specifications. Petri nets are known as efficient mathematical and graphical models that are widely used to describe distributed DES including choices, synchronizations and parallelisms. The domains of application include but are not restricted to manufacturing systems, computer science and transportation networks. Incorporating the time in the model is important to consider many control problems such as scheduling and planning. This paper solves some control issues in timed context and uncertain environments that include unexpected events modeled with uncontrollable transitions. To deal with such uncertainties, we propose first to build an Approximated Timed Reachability Graph that includes the time specifications and model all feasible timed trajectories at a given accuracy under earliest firing policy. Then, this graph is used to search optimal paths by using an approach based on Markov Decision Processes that encode the environment uncertainties. Such optimal paths lead to near-optimal solutions for the TPN. Several simulations illustrate the benefit of the proposed method from the performance and computational points of view.