Control Design for Bounded Partially Controlled TPNs Using Timed Extended Reachability Graphs and MDP

Abstract

This paper is about the design of control sequences for discrete event systems (DESs) modeled with bounded partially controlled timed Petri nets (PC-TPNs) including a set of temporal specifications that correspond to minimal firing durations. Petri nets are well-known mathematical and graphical models that are widely used to describe distributed DESs, including choices, synchronizations, and parallelisms. The domains of application include but are not restricted to manufacturing systems, computer science, and transportation networks. Including the time in the model is important to consider many control problems. This paper is more particularly concerned with control issues in timed context and uncertain environments when unexpected events occur and when control errors disturb the system behavior from the planned policy decided by the controller. To deal with such uncertainties, we propose first to build a timed extended reachability graph (TERG) that includes the time specifications when the PC-TPN behaves with an earliest firing policy. Then, the optimal paths in TERG are found by using an approach based on discrete time Markov decision processes under discounted criterion. Several simulations illustrate the benefit of our method from the computational point of view, in particular for uncertain environments.