Automated guided vehicles (AGVs) are being extensively used for transportation and distribution of materials due to their high-efficiency. However, the vehicle-collision free problem is challenging since, when modeling these systems, there are indistinguishable and uncontrollable events due to the limited sensors and actuators. This paper proposes an approach to the design of a maximally permissive (optimal) controller to prevent vehicles from any collision based on Petri nets (PNs). For a typical class of AGV systems, a system modeling algorithm is presented using labeled PN, where indistinguishable events are represented by a set of transitions carrying the same label, and an uncontrollable event by an uncontrollable transition. By virtue of the PN model, the collision-free problem is formalized as a conjunction of linear constraints that are converted into admissible ones by an algorithm such that the computational overhead due to uncontrollable events is significantly reduced. In turn, a method is developed to compute the set of consistent markings for an observed sequence of labels that represent signals generated by sensors. Finally, given an observed sequence, a maximally permissive control action is computed to enforce a conjunction of admissible linear constraints based on the set of consistent markings. The approach well addresses the challenging issues caused by indistinguishable and uncontrollable events. A typical AGV system is utilized to illustrate and verify the theoretical results throughout the work.

Cell transmission model (CTM) is useful for evaluating the performance of urban traffic networks due to its mathematical formalism. This paper explores the application of CTM to develop control strategies for dispersion accident-induced traffic jams and evaluates the efficiency of these strategies. On the other hand, Timed Petri nets (TPNs) perform in discrete event systems because they provide a balance between modeling power and analyzability. This paper focuses on using the developed TPNs to model variable traffic light control systems. One advantage of the proposed methods is that the traffic light behavior is clearly represented in terms of conditions and events, which result in changes in the pre-emption phase. Moreover, this paper also proposes a new control strategy to eliminate the traffic jam propagation by preventing the traffic flow heading in the direction of an accident. The analysis is performed to demonstrate how the models enforce the phase of traffic transitions by a reachability graph with time information. The liveness and reversibility of the proposed model are verified. To the best of our knowledge, this is the first paper to use TPNs to model a variable phase traffic light control system and identify its accident scenarios for the purpose of their complete avoidance. This helps the latest advanced technology in traffic safety related to the intersection of roadways.

Based on the P-type composition of Petri nets (PN) defined in this paper, a framework for a structuralcontrol of discrete event systems (DES) is constructed such that a closed-loop PN is obtained by composing a plant PN and a controller. As for a disjunction or conjunctive normal form (CNF) of linear constraints, a new approach is proposed to design a structural controller in this framework. First, a switching-net is defined for a disjunction of constraints, and an extended plant is obtained through the P-type composition of a plant PN and switching-net. Second, the disjunction of bounded constraints are transformed into a conjunction of switching-constraints on the extended plant. Third, a controller is synthesized by designing monitors for conjunctive switchingconstraints according to a supervision-based-on-place-invariant method. Fourth, in a similar manner, a controller is also designed for a CNF of bounded constraints. The resulting controller is maximally permissive if each disjunction of constraints meets the jump-free condition, and its size grows polynomially with the number of constraints. Another advantage is that the closed-loop system is still a PN for many real DES since a CNF can describe not only convex but also nonconvex state-regions.